Question

1. A random sample of 25 of the 400 members of the Bigtime Theater

Answer 1

Answer:

Minimum value = 1

Maximum value = 10

First Quartile or 25th percentile = 2.5

Third Quartile or 75th percentile = 5

Median = 4

Inter Quartile Range (IQR) = 2.5

Range = 9

Number of variables = 25

Outliers = 10

Step-by-step explanation:

Note that a box and whiskers plot shows 5 major information about the distribution of data. It shows:

- The maximum variable

Simply the maximum value of the distribution.

This is usually read from the whiskers, the tail end on the whiskers at the top of the plot. But this distribution has an outlier (represented by the singular dot, which can now serve as the maximum value. Maximum value = 10

- The minimum variable

Simply the minimum value of the distribution.

This is also easily read from the whiskers, the very beginning of the whiskers at the bottom. For this distribution, the minimum value is 1.

- The first Quartile or the 25th percentile

This is the beginning of the boxplot. For this distribution, it is 2.5.

- The third quartile or the 75th percentile

This is the end of the boxplot. For this distribution, it is 5.

- The Median

This is the number at the middle of the distribution when all the variables are arranged in ascending or descending order.

This is represented by the point that coincides with the line drawn on the boxplot. For this distribution, the Median is 4.

The other variables describing the dataset that can be obtained from the boxplot include;

1) The Interquartile Range (IQR)

The IQR is a measure of the spread of the distribution and it is given mathematically as the difference between the third and first quartile.

IQR = (Third quartile or 75th percentile) - (First quartile or 25th percentile)

IQR = 5 - 2.5 = 2.5

2) The range.

The range is given as the difference between the maximum and minimum values of a distribution.

Range = (Maximum value) - (Minimum Value) = 10 - 1 = 9.

Hope this Helps!!!