Question

A newspaper article reported that a computer company has unveiled a new tablet computer marketed specifically to school districts for use by students. The new tablets will have faster processors and a cheaper price point in an effort to take market share away from a competing company in public school districts. Suppose that the following data represent the percentages of students currently using the company's tablets for a sample of 18 U.S. public school districts. (Round your answers to two decimal places.)

13 20 10 19 24 16 40 27 62 18 13 20 16 22 25 22 24 17

(a) Compute the mean and median percentage of students currently using the company's tablets. mean % ___median % ___

(b) Compute the first and third quartiles (as percentages) for these data. Q1 % ___ Q3 % ____

(c) Compute the range and interquartile range (as percentages) for these data. range %____ interquartile range %____

(d) Compute the variance and standard deviation (as a percentage) for these data. variance ____standard deviation % ____

(e) Are there any outliers in these data? There____ below the lower limit and _____above the upper limit.

(f) Based on your calculated values, what can we say about the percentage of students using the company's tablets in public school districts?

a. Use of the tablets is very low for all school districts.

b.Use of the tablets is very high for all school districts.

c. Relative to the mean, there are some school districts where many more students are using the tablets.

d.Relative to the mean, there are some school districts where much fewer students are using the tablets.

e.Relative to the mean, use of the tablets is similar for all school districts.

Answer 1

In ascending order, the data set will be

10 13 13 16 16 17 18 19 20 20 22 22 24 24 25 27 40 62

a) mean = (10 + 13 + 13 + 16 + 16 + 17 + 18 + 19 + 20 + 20 + 22 + 22 + 24 + 24 + 25 + 27 + 40 + 62)/18 = 22.67

Median = (20 + 20)/2 = 20

b) Q1 = 16

Q3 = 24

c) range = 62 - 10 = 52

IQR = Q3 - Q1 = 24 - 16 = 8

d) Variance = ((10 - 22.67)^2 + (13 - 22.67)^2 + (13 - 22.67)^2 + (16 - 22.67)^2 + (16 - 22.67)^2 + (17 - 22.67)^2 + (18 - 22.67)^2 + (19 - 22.67)^2 + (20 - 22.67)^2 + (20 - 22.67)^2 + (22 - 22.67)^2 + (22 - 22.67)^2 + (24 - 22.67)^2 + (24 - 22.67)^2 + (25 - 22.67)^2+ (27 - 22.67)^2 + (40 - 22.67)^2 + (62 - 22.67)^2)/17 = 140.82

Standard deviation = = 11.87

e) Q1 - 1.5 * IQR = 16 - 1.5 * 8 = 4

Q3 + 1.5 * IQR = 24 + 1.5 * 8 = 36

The outliers are 40 and 62.

There is no data value below the lower limit and 2 data value above the upper limit.

f) Option - c) Relative to the mean, there are some school districts where many more students are using the tablets.