ic 4 Measures of dispersion An accounting professor taught three sections of principles of accounting, She gave a midterm examination in each of the three sections, The mean scores for the three sections were 29, 41, and 37, respectively. The standard deviations for the three sections were 8.2, 8.7, and I1 respectively. Which section had the greatest relative dispersion? Why? Janna Vice uses two different machines to produce paper chutes for Kodak copiers. A sample of the chutes from the first machine measured 12.2, 11.9, 11.8, 12.1, 11.9, 12.4, 11.3, and 12.3 inches. Chutes made with the second machine measured 12.2, 11.9, 11.5, 12,1, 12.2, 11.9, and 11.8 inches. Janna must use the machine with the greater consistency in sizes of the chutes. Which machine should she use? Why? A personnel manager wants to determine whether managers or staffs have more variability in their salaries. Consequently, the manger has obtained a respective set of monthly salaries from each category. Managers: 2500 1840 1750 2100 2225 Staffs: 1100 1050 1200 1090 1050 1125 1320 Which group shows the greater relative variation? Why? Measurement made with one (first) micrometer of the diameter of a ball bearing have a mean of 3.92 mm and a standard deviation of 0.015 mm, where as measurements made with another (second) micrometer of the un stretched length of spring have a mean of 1.54 inches and a standard deviation of 0.008 inch. Which of these two measuring instruments is relatively more precise? 4 m F5 07 W $ 5 5 Q F6 % F7 S Ron 9# music Warfra 5) Which of the following is correct? a) b ) Measures of dispersion describe typical values in the data. The coefficient of variation is useful in comparing the relative dispersion C ) . for the distribution involving different units of measurement. d) In a symmetrical distribution, the median will be greater than the mean. When a distribution has a great many values clustered to the left and tails of the right, it is said to be negatively skewed. 6). A disadvantage of using a range is that.... a ) . it is influenced by extreme values. b ) . it is determined by only two points in the data set. C ) . it is difficult to calculate. d) . (a) and (b) 7 ). The mean deviation is a ). based on squared deviations from the mean. b ) also called the variance. C ) . based on absolute values. d) None of the above 8). True or False a) The value of variance and standard deviation are never zero. b ) Mean and range are influenced by extreme values. C) For an asymmetric distribution, if there is a longer tail to right-hand side, the distribution is said to be positively skewed. d). When the variable studied can be reported numerically, the variable is called qualitative variable. The order that runners finish in a race would be an example of ordinal level. e ) . A relative frequency distribution shows the number of occurrence in each class. Number 3, 4, 5, have a smaller standard deviation than 1003, 1004, 1005. g). The standard deviation can only be computed for interval or ratio level data. h). i). Mean can be calculated for nominal and ordinal level data. j). Standard deviation never greater than the range of data. Fill in distribution, each of the class 1). To convert a frequency distribution to a frequencies is divided by the total number of observations. is (are) unaffected 2 ) . Among the measures of central tendency (location) by extreme values. 3 ) . The can be founded for nominal level of data. 4 ). In a skewed distribution, the mean is the largest of the three averages. 5 ) . The mean of the squared deviations from the mean is 6). The square root of the variance is called the 7 ) . A useful measure to compare the relative dispersion in two or more distributions, if they are in different units, is the 8) is the most widely used measures of central tendency (location). 9 ) . In what order will the mean, median, and mode occur in a distribution that is skewed to the right? 9is the most widely reported measures of dispersion . 10). is based on only two values, the highest I1). Among the measures of dispersion, and the lowest, it does not take into consideration all of the values. is the ratio of the standard deviation to the mean expressed in percentage. 12). 13). is the ration of frequency of that class to the total frequency. 14). The level of measurement presumes that one category is ranked higher than other. 15). If the median is substantially higher than the mean, in which direction is the distribution skewed? 16). Among the measures of central tendency (location), is applicable for both qualitative and quantitative data.CHAPTER 1- 4 Review 1. For each of the following variables, indicate whether they are discrete or continuous variable. a)A tailor uses a tape measure to determine exactly where to cut a piece of cloth. b) The number of siblings you have. c) A number of cans. d) A tomato weight. 2. Classify a type ( qualitative or quantitative ) and a level of data ( nominal, ordinal , interval , or ratio level ) for each of the following variables. Type of data Level of data a) Arranging the books in the library subject wise , author wise b) Development time in hours c) General happiness ( very happy, pretty happy, not too happy ) d) Goals scored by Brazil in the World Cup 3. Fill in the blanks. a) The front row in a movie theatre has 23 seats. If you were asked to sit in the seat that occupied the median position, in which seat would you have of sit ? b) The production manager for a manufacturer of glass jars, who is concerned about the proper jar size to manufacture, has sample data on jar sizes ordered by customers. Which measure of central tendency ( location) jar size would be of most value to the manager ? - c) In a group of 5 scores, the largest score is increased by 15 points. The mean of the score will be ( increased, decreased ) by - points. d) Among the measures of central tendency ( location ) - is ( are ) applicable for both qualitative and quantitative data. ) The most general measure of variability is3. Mary ordered dinner for a party of 10 people. Three people ordered the $ 4.75 chicken dinner, two people ordered the $ 4.95 fish dinner, and five had the beef dinner at a cost of $ 6.75 each. What was the average cost of each dinner at Mary's party? 4. The average monthly salary of 12 workers and 3 managers in a factory was $ 600. When one of the manager whose salary was $ 720, was replaced with a new manager, then the average salary of the team went down to $ 580. What is the salary of the new manager ? 5. The following frequency distribution shows the price of blouse for a sample of 20 women bought last month. Price ( $ ) Frequency 10 4 15 W 20 25 HWUTA 30 35 a) The median value of price is b) The modal value of price is c) What percentage of women in this sample bought not more than $ 25 price ? - 6. Leon and John went bowling. Their scores are given below. Leon : 148 201 165 120 210 John : 123 189 220 187 210 a) Who had the greater median scores? What was the greater median scores ? b) Who had the higher average score? What was the higher average score ?7. A service station has recorded the following table for the number of gallons of gasoline sold per car, Gasoline ( gallons )| Number of cars Cumulative frequency less than type more than type 0-4 14 5-9 266 10- 14 546 15 - 19 651 20 - 24 674 25 - 29 68O a) How many cars were involved in the surveyed? ammazzumessage b) Set the column of number of cars, c) Set the column of cumulative frequency ( more than type ), d) The mean gallons of gasoline is #manages e) The median Value is -mmmmmmwas" ( show your work briefly ) f) The modal value is -mmmmmm g) The sample standard deviation value is --..--... 8. The following is a sample of 40 students Math test results marked out of 10 points. Score 1 2 6 7 8 10 Frequency 2 3 2 10 3 6 2 a) How many students get more than 5 points? ammmmmmmmmmmmm students b) The value of median score is --.--.--." c) The value of mode score is