Question

Calculate the mean, median, mode, range, and 5 Number Summary of the following data set:

Answer 1

Answer:

1. Mean = 4.57

2. Median = 5

3. Mode = 5

4. Range = 7

Five Number Summary

5. Minimum = 1

6. First Quartile = 4

7. Median = 5

8. Third Quartile = 6

9. Maximum = 8

Step-by-step explanation:

Let's arrange the numbers in order (smallest to largest):

1,2,2,4,4,4,5,5,5,5,6,6,7,8

We need to find:

1. mean

2. median

3. mode

4. range

Five Number Summary

5. Minimum

6. First Quartile

7. Median

8. Third Quartile

9. Maximum

1.

Mean is the sum of all the numbers divided by the number of numbers.

Mean = $\frac{1+2+2+4+4+4+5+5+5+5+6+6+7+8}{14}=\frac{64}{14}=4.57$

Mean is 4.57

2.

Median is the "middle" number when the data set is arranged in order (already done).

There are 14 numbers, so the middle number would be the average of the 7th and 8th number.

7th number is 5

8th number is 5

Average is (5+5)/2 = 5

Thus, Median = 5

3.

Mode is the number that occurs the MOST. Looking at the range, the "most" occuring number is 5 (it appeared 4 times).

Mode = 5

4.

Range is the highest value minus the lowest value.

Highest value is 8

lowest value is 1

Thus, Range = 8 -1 = 7

Range = 7

Five Number Summary

5.

Minimum value is the lowest value. Thus minimum value is 1.

Minimum = 1

6. First Quartile is the value that is 1/4th. In a total of 14 numbers, the 1/4th value would be 1/4*14 = 3.5. We round to the next number, which is 4th.

Thus, 4th value in the data set is 4.

First Quartile = 4

7.

Median have already been found to be 5.

Median = 5

8. Third quartile is the value that is 3/4th. In a total of 14 numbers, the 3/4th value would be 3/4*14 = 10.5. We round to the next number, which is 11th.

THus, 11th value in the data set is 6.

Third Quartile = 6

9.

The maximum value is the highest value. Looking at the data set, it is 8.

THus, maximum = 8