Questions and Answers of Descriptive Statistics

15 students do a mathematics test. Their marks are shown opposite. a Find the value of the median. 7 4 9 10 5 29 12 11 8 737 683b. Find Q and Q c Work out the interquartile range.AppendixLO1
A group of workers were asked to write down their weekly wage. The wages were: 550 400 260 320 500 450 a Work out the range for these wages. b Find Q and Q. 460 480 510 490 505 c Work out the
A superstore records the number of hours overtime worked by their employees in one particular week. The results are shown in the table. a Fill in the cumulative frequency column and work out how many
A moth trap was set every night for five weeks. The number of moths caught in the trap was recorded. The results are shown in the table. Number of moths Frequency 7 2 8 5. 9 9 10 14 11 5 Find the
The weights of 31 Jersey cows were recorded to the nearest kilogram. The weights are shown in the table. Weight of cattle (kg) Frequency Cumulative frequency 300-349 3 350-399 6. 400-449 10 450-499 7
The number of visitors to a hospital in a week was recorded. The results are shown in the table. Number of visitors Frequency 500-1000 10 1000-1500 25 1500-2000 15 2000-2500 5 2500-3000 5 Giving your
The lengths of a number of slow worms were measured, to the nearest mm. The results are shown in the table. a Work out how many slow worms. were measured. b Find the interquartile range for the
A gardener counted the peas in a number of pea pods. The results are shown in the table. Number Frequency of peas Cumulative frequency 6 8 7 12 8 36 9 18 10 15 11 10 a Complete the cumulative
A shopkeeper goes to a clothes fair. He records the costs of jeans. The costs are shown in the table. Cost of jeans (E's) Frequency Cumulative frequency 10-15 11 16-20 35 21-25 34 26-30 16 31-35 10
The table shows the monthly income for a number of workers in a factory. Calculate the 34% to 66% interpercentile range. Monthly income ('s) Frequency 900-1000 3 1000-1100 24 1100-1200 28 1200-1300
A train travelled from Lancaster to Preston. The times, to the nearest minute, it took for the journey were recorded over a certain period. The times are shown in the table. Time for journey
A roadside assistance firm kept a record over a week of the amount of time, in minutes, people were kept waiting for assistance in a particular part of the country. The time taken was from the time
Given that for a variable x: 24 Find: Ex-78 11-8 b The variance o a The mean. The standard deviation o AppendixLO1
Ten collie dogs are weighed (w kg). The following summary data for the weights are shown below: w=241 w=5905 Use this summary data to find the standard deviation of the collies' weights.AppendixLO1
Eight students' heights (h cm) are measured. They are as follows: 165 170 190 180 175 185 176 a Work out the mean height of the students. 184 b Given h 254 307 work out the variance. Show all your
For a set of 15 numbers: = 86 = 568 Find the mean and the standard deviation of the combined set of 25 numbers.AppendixLO1
The number of members (m) in six scout groups was recorded. The summary statistics for these data are: m-150 m-3846 a Work out the mean number of members in a scout group. b Work out the standard
There are two routes for a worker to get to his office. Both the routes involve hold ups due to traffic lights. He records the time it takes over a series of six journeys for each route. The results
For a certain set of data: 1975 fx-52325 Work out the variance for these data.AppendixLO1
For a certain set of data fx-264 fx-6456 -100 -12 Work out the standard deviation for these data.AppendixLO1
Nahab asks the students in his year group how much pocket money they get per week. The results, rounded to the nearest pound, are shown in the table. Number of Number of fx E's (x) students f 8 14 9
In a student group, a record was kept of the number of days absence each student had over one particular term. The results are shown in the table. Number days Number of absent (x) fx students f 0 12:
A certain type of machine contained a part that tended to wear out after different amounts of time. The time it took for 50 of the parts to wear out was recorded. The results are shown in the table.
The heights (x cm) of a group of 100 women were recorded. The summary data is as follows: 17 100 fx-2926225 Work out the variance and the standard deviation.AppendixLO1
a Work out the standard deviation of the following data. x 11 11 13 13 15 20 25 b Use the following coding to find the standard deviation of the data. Show all the working. ix-10 ii x 10 iii x-3 2
Use the following codings to find the standard deviation of the following weights, w. W 210 260 310 360 410 W ii w - 200 iii 10 w-10 200 3 a AppendixLO1
The coding y x-50 28 gives a standard deviation of 0.01 for y. Work out the standard deviation for x. h b The coding y produced a standard deviation for y of 0.045. What is the standard deviation of
The coding y=x-14 produced a standard deviation for y of 2.37. What is the standard deviation of x? d The coding y=-5, 10 produced a standard deviation for y of 0.65. What is the standard deviation
The lifetime, x, in hours, of 70 light bulbs is shown in the table. Lifetime in Number of light bulbs hours 20-22 3 22-24 12 24-26 40 26-28 10 28-30 5 total. 70 Using the coding y x-1 estimate the
The weekly income, i, of 100 women workers was recorded. i-90 The data were coded using y=100 and the following summations were obtained. = 131, = 176.84 Work out an estimate for the standard
For the set of numbers: 25389 10 3 2 15 10 5 7 675 a work out the median, b work out the lower quartile, e work out the upper quartile, d work out the interquartile range.AppendixLO1
A frequency distribution is shown below Class interval 1-20 21-40 41-60 61-80 81-100 Frequency (f) 5 10 15 12 8 Work out the interquartile range.AppendixLO1
A frequency distribution is shown below. Class interval 1-10 11-20 21-30 31-40 41-50 Frequency (f) 10 20 30 24 16 a Work out the value of the 30th percentile. b Work out the value of the 70th
The heights(h) of 10 mountains were recorded to the nearest 10m and are shown in the table below. h1010 1030 1050 1000 1020 1030 1030 1040 1020 1000 Use the coding y-10 to find the standard deviation
The times it took a random sample of runners to Time taken complete a race are summarised in the table. (t minutes) Frequency a Work out the lower quartile. 20-29 5 b Work out the upper quartile.)
20 birds were caught for ringing. Their wing spans (x) were measured to the nearest centimetre. The following summary data was worked out: = 316 = 5078 a Work out the mean and the standard deviation
The heights of 50 clover flowers are summarised in the table. Heights in mm (h) Frequency 90-95 5 95-100 10 100-105 26 105-110 8 110-115 1 a Find Q. b Find Q. c Find the interquartile range. d Use fx
A group of thirty college students was asked how many DVDs they had in their collection. The results are as follows. 12 25 34 17 12 18 29 34 45 6 15 925 23 29 22 20 32 15 15 19 12 26 27 27 32 35 42
The following stem and leaf diagram shows some information about the marks gained by a group of students in a statistics test. stem leaf 0 89 Key: 23 means 23 marks (2) 1 25 59 2 36 6 6 7 3 4 4 5 7 7
The number of laptops sold by a store was recorded each month for a period of 26 months. The results are shown in the stem and leaf diagram. Key: 18 means 18 laptops stem leaf 1. 8 2 3 6 79 9 3 26667
A class of 16 boys and 13 girls did a Physics test. The test was marked out of 60. Their marks are shown below. Boys Girls 45 54 32 60 26 54 47 32 28 34 54 56 34 34 45 46 32 29 47 48 39 52 24 28 44
The following stem and leaf diagram shows the weekend earnings of a group of college students. Males 8 765 Females Key: 5|1|0 means 15 for males 0 6 and 10 for females 1055588 2 5 5 8 8 9 88555 3 5 5
Some data are collected. The lower quartile is 46 and the upper quartile is 68. An outlier is an observation that falls either 1.5 x (interquartile range) above the upper quartile or 1.5 x
Male and female turtles were weighed in grams. For males, the lower quartile was 400 g and the upper quartile was 580 g. For females, the lower quartile was 260 g and the upper quartile was 340 g. An
A group of students took a statistics test. The summary data for the percentage mark gained by boys and by girls is shown in the box plots opposite. a Write down the percentage mark which 75% of the
Male and female turtles were weighed in grams. Their weights are summarised in the box plots opposite. a Compare and contrast the weights of the male and female turtles. b A turtle was found to be
The heights of a year group of children were measured. The data are summarised in the group frequency table. Height (cm) Frequency Class width Frequency density 135-144 40 10 145-149 40 5 150-154 75
Some students take part in an obstacle race. The time it took each student to complete the race was noted. The results are shown in the histogram.a Give a reason to justify the use of a histogram to
The time taken for each employee in a company to travel to work was recorded. The results are shown in the histogram.The number of employees who took less than 10 minutes to travel to work is 48. a
A Fun Day committee at a local sports centre organised a throwing the cricket ball competition. The distance thrown by every competitor was recorded. The data were collected and are shown in the
A farmer weighed a random sample of pigs. The weights were summarised in a grouped frequency table and represented by a histogram. One of the classes in the grouped frequency distribution was 28-32
In a survey of the earnings of some sixth form students who did Saturday jobs the median wage was 36.50. The 75th percentile was 45.75 and the interquartile range was 30.50. Use the quartiles to
A group of estate agents recorded the time spent on the first meeting with a random sample of 120 of their clients. The times, to the nearest minute, are summarised in the table. a Calculate
The following stem and leaf diagram summarises the wing length, to the nearest mm, of a random sample of 67 owl moths.a Write down the mode of these data. b Find the median and quartiles of these
A TV company wishes to appeal to a wider range of viewers. They decide to purchase a programme from another channel. They have the option of buying one of two programmes. The company collects
Jason and Perdita decided to go for a touring holiday on the continent for the whole of July. They recorded the number of kilometres they travelled each day. The data are summarised in the stem and
Sophie and Jack do a survey every day for three weeks. Sophie counts the number of pedal cycles using Market Street. Jack counts the number of pedal cycles using Strand Road. The data they collected
Shop A and Shop B both sell mobile phones. They recorded how many they sold each day over a long period of time. The data they collected are represented in the box plots. a Shop B says that for 50%
Fell runners from the Esk Club and the Irt Club were keen to see which club had the fastest runners overall. They decided that all the members from both clubs would take part in a fell run. The time
The histogram shows the time taken by a group of 58 girls to run a measured distance. a Work out the number of girls who took longer than 56 seconds. b Estimate the number of girls who took between
The table gives the distances travelled to school, in km, of the population of children in a particular region of the United Kingdom.A histogram of this data was drawn with distance along the
The labelling on bags of garden compost indicates that the bags weigh 20 kg. The weights of a random sample of 50 bags are summarised in the table opposite. a On graph paper, draw a histogram of
The number of bags of potato crisps sold per day in a bar was recorded over a two-week period. The results are shown below. 20 15 10 30 33 40 5 11 13 20 25 42 31 17 a Calculate the mean of these
Throwing a six sided die once and recording if the number face up is odd or even. Find the probability of an even number landing face up.AppendixLO1
Tossing two coins. Find the probability of the same outcome on each coin.AppendixLO1
A card is drawn from a pack of 52 playing cards. Find the probability that the card is a heart.AppendixLO1
A card is drawn from a pack of 52 playing cards, its suit is recorded then it is replaced and another card is drawn. Find the probability of drawing a spade and a club in any order. 5 Throwing a die
Throwing two six sided dice and recording the product of the values on the two sides that are uppermost. Find the probability of the answer being greater than or equal to 24.AppendixLO1
A card is chosen at random from a pack of 52 playing cards. C is the event 'the card chosen is a club' and K is the event 'the card chosen is a King'. Find these. a P(K) d P(CUK) b P(C) e P(C') c
There are 25 students in a certain tutor group at Philips College. There are 16 students in the tutor group studying German, 14 studying French and six students studying both French and German. Find
On a firing range, a rifleman has two attempts to hit a target. The probability of hitting the target with the first shot is 0.2 and the probability of hitting with the second shot is 0.3. The
Of all the households in the UK, 40% have a plasma TV and 50% have a laptop computer. There are 25% of households that have both a plasma TV and a laptop. Find the probability that a household chosen
There are 125 diners in a restaurant who were surveyed to find out if they had ordered garlic bread, beer or cheesecake. 15 diners had ordered all three items 43 diners had ordered garlic bread 40
A group of 275 people at a music festival were asked if they play guitar, piano or drums. one person plays all three instruments 65 people play guitar and piano 10 people play piano and drums 30
A and B are two events and P(A) = 0.5, P(B) = 0.2 and P(AB) = 0.1. Find a P(AUB), P(AB), b P(B), d P(A U B').AppendixLO1
A and C are two events and P(A) = 0.4, P(B) = 0.5 and P(AUB) 0.6. Find a P(AB), C P(A U B'), b P(A'), d P(A' UB).AppendixLO1
C and D are two events and P(D) = 0.4, P(CD) = 0.15 and P(C n D) = 0.1. Find a P(CD), e P(C),b. P(CD), d P(CD).AppendixLO1
There are two events T and Q where P(T) = P(Q) = 3P(TQ) and P(TUQ) = 0.75. Find a P(TQ), d P(TQ), b P(T), e P(TQ). c P(Q), AppendixLO1
A survey of all the households in the town of Bury was carried out. The survey showed that 70% have a freezer and 20% have a dishwasher and 80% have either a dishwasher or a freezer or both
The probability that a child in a school has blue eyes is 0.27 and the probability they have blonde hair is 0.35. The probability that the child will have blonde hair or blue eyes or both is 0.45. A
A patient going in to a doctor's waiting room reads Hiya Magazine with probability 0.6 and Dakor Magazine with probability 0.4. The probability that the patient reads either one or both of the
A card is drawn at random from a pack of 52 playing cards. Given that the card is a diamond, find the probability that the card is an ace.AppendixLO1
Two coins are flipped and the results are recorded. Given that one coin lands on a head, find the probability of a two heads,b. a head and a tail.AppendixLO1
Two fair dice are thrown and the product of the numbers on the dice is recorded. Given that one die lands on 2, find the probability that the product on the dice is a exactly 6, b more than
A and B are two events such that P(A) b P(B|A), a P(AUB), AppendixLO1
A and B are two events such that P(A) a P(B|A), b P(AB), AppendixLO1
Let A and B be events such that P(A) = Find a P(A|B), b P(AB), AppendixLO1
C and D are two events and P(CID) = a P(CD), b P(CD), P(A|B), 0.6, P(B) 0.5 and P(A B) -0.4, find d P(A|B'). 0.4, P(B) - 0.5 and P(A|B) 0.4, find c P(AB). P(B) = and P(AUB) = C PA'B'). P(CID) and
A bag contains five red and four blue tokens. A token is chosen at random, the colour recorded and the token is not replaced. A second token is chosen and the colour recorded. Find the probability
A box of 24 chocolates contains 10 dark and 14 milk chocolates. Linda chooses a chocolate at random and eats it, followed by another one. Fine the probability that Linda eats a two dark chocolates, b
Jean always goes to work by bus or takes a taxi. If one day she goes to work by bus, the probability she goes to work by taxi the next day is 0.4. If one day she goes to work by taxi, the probability
Sue has two coins. One is fair, with a head on one side and a tail on the other. The second is a trick coin and has a tail on both sides. Sue picks up one of the coins at random and flips it. a Find
A contestant on a quiz show is asked to choose one of three doors. Behind one of the doors is the star prize of a sports car, but behind each of the other two doors there is a toy car. The contestant
Event A and event B are mutually exclusive and P(A) = 0.2, P(B) = 0.5. a Draw a Venn diagram to represent these two events. b Find P(AUB). c Find P(A' n B').AppendixLO1
Two events A and B are independent and P(A) and P(B) - Find a P(AB),b. P(AB), AppendixLO1
Q and R are two events such that P(Q) a the relationship between Q and R, C P(A'B'). 0.2, P(R) = 0.4 and P(QR) = 0.4. Find b P(QUR), P(QR).AppendixLO1
Two fair dice are rolled and the result on each die is recorded. Show that the event 'the sum of the scores on the dice is 4' and' both dice land on the same number' are not mutually
A bag contains three red beads and five blue beads. A bead is chosen at random from the bag, the colour is recorded and the bead is replaced. A second bead is chosen and the colour recorded. a Find
A box contains 24 electrical components of which four are known to be defective. Two items are taken at random from the box. Find the probability of selecting a two defective components if the first
A bag contains one red, two blue and three green tokens. One token is chosen at random, the colour is recorded and the token replaced. A second token is then chosen and the colour recorded. a Draw a

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