Chapter 1: Q 2.1. (page 34)

1. Use the back-to-back stemplot in Figure $1.15$ to write a few sentences comparing the number of pairs of shoes owned by males and females. Be sure to address shape, center, spread, and outliers.

Short Answer

Expert verified

The male data has a bimodal distribution, while the female data has a unimodal distribution. The center of male and female information is as follows $11.5$ and $30.3$ The spread of the Interquartile Range of the male is $5$ and the Interquartile Range of females is $23$ The outliner for male information is $22, 35, 38$ and for female information is $57$

Step by step solution

Given information

To calculate the number of pairs of shoes which are owned by males and females, the below graph will be helpful.

Calculation

The calculation from the provided data from the stem plot for male is

$4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 10, 10, 10, 10, 11, 12, 14, 22, 35, 38$

The provided data from the stem plot for female is

$13, 13, 13, 15, 19, 22, 23, 23, 24, 26, 26, 30, 31, 34, 38, 49, 50, 50, 51, 57$

Shape:

For male data $(4)$ , the maximum times were $7$ and $10$ .. So there are two modes in this data. In other words, the male data has a bimodal distribution.

Only $13$ women have reached the maximum amount of time allowed for female data $(3)$ . As a result, there is just one mode in this data. In other words, the distribution of female data is unimodal.

Centre:The mean for male information is:

$(4 + 5 + . . . . . + 38) / 20 = 233 / 20 = 11.65$

The mean for female information is: $= (13 + 13 + . . + 51 + 57) / 20 = 607 / 20 = 30.3$

Spread:

The information range for males is $= 38 - 4 = 34$

The Standard deviation is $= 9.18$

$1^{s t}$ Quartile is $Q_{1} = 6.5$

$2^{n d}$ Quartile is $Q_{2} = 9$

$3^{r d}$ Quartile is $Q_{3} = 11.5$

Interquartile Range is:

$I Q R = Q_{3} - Q_{1} = 11.5 - 6.5 = 5$

The information range for female $= 57 - 13 = 44$

The Standard deviation is $= 13.88$

$1^{s t}$ Quartile is $Q_{1} = 20.5$

$2^{n d}$ Quartile is $Q_{2} = 26$

$3^{rd}$ Quartile is $Q_{3} = 43.5$

Interquartile Range is

$I Q P = Q_{3} - Q_{1} = 43.5 - 20.5 = 23$

Outliners:

For information on males

Outliers are values that go outside of $(Q_{1} - 1.5 I Q R, Q_{3} + 1.5 I Q R)$ , resulting in $(4, 14)$ .

The outliers are as follows: $22, 35, 38$

Women's information Outliers are values that go outside of $(Q_{1} - 1.5 I Q R, Q_{3} + 1.5 I Q R)$ , resulting in $(9, 55)$ .

The following are the outliers: $57$

Concept

Shape: The peak of the dot plot is at This means that during that season, the team's most common number of goals scored in games (known as the mode) was The United States women's soccer team scored between one and five goals in the majority of its games. The distribution, however, has a large tail to the right.

Centre: can be described by selecting a value that divides the observations in half, with the bigger half taking greater values and the smaller half taking lower values.

Spread: distribution indicates the amount of variability in the data. Giving the smallest and greatest values is one approach to describe the variability.

Outlier: is a value that is notably different from other values in a random sampling of the population.