A sample of $10$ adults was asked to report the number of hours they spent on the Internet the previous month. The results are listed below:

$0,7,12,5,44,14,8,0,9,56$

Calculate the mean, median and the mode $($if any$).$

Compute the variance and standard deviation.

Column$1$

Mean $15\mathrm{.}5$

Standard Error $5\mathrm{.}989342$

Median $8\mathrm{.}5$

Mode $0$

Standard Deviation $18\mathrm{.}93996$

Sample Variance $358\mathrm{.}7222$

Kurtosis $1\mathrm{.}576783$

Skewness $1\mathrm{.}627556$

Range $56$

Minimum $0$

Maximum $56$

Sum $155$

Count $10$

Calculate first, second, and third quartiles.

Determine the interquartile range.

Q$12\mathrm{.}5$

Q$28\mathrm{.}5$

Q$329$

IQR $26\mathrm{.}6$

Interpret the obtained results.

Mean$=15\mathrm{.}5,$ the average number of hours people spent on the Internet, means that most of the adults spent on the internet about $15\mathrm{.}5$ hours per month.

Median$=8\mathrm{.}5,$ the half of all hours spent by people on the Internet is below $8\mathrm{.}5$ hours, the other half is above this value.

Mode$=0,$ the most frequent number of hours that people spent in the Internet.

Variance$=358\mathrm{.}72,$ the value shows how far a set of the given hours is spread out far away from their average value $($mean$).$

Standard deviation$=18\mathrm{.}94,$ shows how values of the sample deviate from the sample mean.

Q$1=2\mathrm{.}5,$ one quarter of adults spent below $5\mathrm{.}5$ hours, while the remaining spent above $5\mathrm{.}5$ hours.

Q$3=29,$ three quarters of the adults spent below $13\mathrm{.}5,$ while the other quarter spent above $13\mathrm{.}5.$

IQR$=26\mathrm{.}5,$ shows the range of the middle $50\%$ of Internet hours.

Solving Problems

The ages of the employees of a fast$-$food outlet are as follows:

$19,19,65,20,21,18,20,35,42,55,37,23,45,48,50$

$32,40,56,39,20,22,27,28,30,51,63,59,23,34,35$

Draw the stem and leaf display to these data.

Build a frequency distribution with $5$ class.

Construct a frequency histogram and a frequency curve for the grouped data created in part b$.$

To study a waiting time in minutes that spend to serving customers during the peak lunch period, a random sample of $15$ customers is selected, and the results are listed in the following frequency distribution.

Class intervals Number of customers Class marks Class boundaries Relative frequencies Cumulative frequencies

$0-44$

$5-96$

$10-143$

$15-192$

Total

Dress the class marks, the class boundaries, the relative frequencies and the cumulative frequencies of the waiting time.

What the number $3$ which corresponds to the class interval $10-14$ represents?

Draw an ogive to the above data.

What percentage of customers waiting for at most $9$ minutes during the peak lunch period?

The following are the frequency distribution of the time in days required to complete year$-$end audits:

Audit time $($days$)$ Frequency

$10144$

$15198$

$20245$

$25292$

$30341$

a$.$ Draw a frequency histogram.

b$.$ Describe the data of this distribution

c$.$ Construct a cumulative relative frequency distribution.

d$.$ Draw an ogive

e$.$ Estimate the number of audits that required to be completed in $17$ days

$.$

Suppose that a factory producing the batteries. From the factory production, $11$ batteries are drawn to test for the lifetime $($in hours$).$ These lifetimes are:

$16,9,5,7,14,6,15,4,13,9,12.$

Calculate the mean lifetime.

Compute the variance.

Calculate the standard deviation.

Compute the coefficient of variation.

Determine the first quartile.

Find the median.

Determine the $75$th percentile.

Compute the range.

A sample of $7$ mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below.

$514629112$

a$.$ Calculate and interpret the value of the mean.

b$.$ Compute the variance.

c$.$ Calculate and interpret the standard deviation.

d$.$ Compute the coefficient of variation.

e$.$ Determine the $25$th percentile.

f$.$ Find the median

g$.$ Determine the third quartile.

h$.$ Compute the range.

k$.$ Find the mode $($if any$)$

j$.$ Using the Empirical Rule, about $95$ percent of the ages are between

what two values?

The following is a list of one bowler$$s most recent scores: $-$

$103,92,99,76,81,92,100,92,121,76,91.$

Calculate the mean, median and the mode $($if any$).$

Compute the variance and standard deviation.

Obtain the coefficient of variation.

Find the $75$th percentile.

Determine the first quartile.

Compute the range and the interquartile range.

Determine the $25$th percentile.

Determine the third quartile.

Compute the range and the interquartile range.

Using the Empirical Rule, about $68$ percent of the ages are between what two values