Boxplot find median percentile max min range Please show wor

Boxplot: find median, percentile, max, min, range

Please show work. Thank you.

Problem(8) A boxplot is given on next page, answer the following questions. (a) Estimate the median of the sample. (b) Estimate the 25th percentile of the sample. (c) Estimate the 75th percentile of the sample. (d) Estimate the interquartile range of the sample. (e) Is (Are) there any outlier(s) in the sample. Estimate its (their) value(s). (By default, an outlier is a value that is more than 1.5 times the interquartile range away from the top or bottom of the box.) (f) Disregard the outliers, estimate the maximum of the sample. (g) Disregard the outliers, estimate the minimum of the sample. (h) Disregard the outliers, estimate the range of the sample. (i) Do you think the median and the mean of the sample are close? Please explain.

Solution

1. Median is the middle line in the box. So Median = 117

2. 25th percentile is the lower line of the box, 25th percentlie = 115

3. 75th percentile is the upper line of the box, 75th percentlie = 120

4. Interquartile range = 75th percentile - 25th percentile = 120 -115 =5

5. 3 outliers : 91, 135, 139

6. Maximum is the horizontal line above box, maximum = 125

7. Minimum is the horizontal line below box, minimum = 109

8. Range= Maximum - Minimum = 125 - 109 = 16

9. The median and the mean are close as the distribution is close to symmetrical, that is, the median is at the mid point of the quartiles as well as the middle of the maximum and minimum values.