Question

Some researchers developing a new Intelligence test are trying to decide how much time to allow to complete the test. The researchers have recorded the times(in minutes) for completion of 26 people who took the test for practice. The frequency distribution below summarizes the completion times recorded by theresearchers.Time for completion(in minutes)Frequency9 to 1112 to 14715 to 1785318 to 2021 to 233Based on the frequency distribution, using the midpoint of each data class, estimate the mean completion time of the people who took the test. For yourintermediate computations, use four or more decimal places, and round your answer to one decimal place.

Answer 1

To find the mean of grouped data, we need to use the next formula:

`Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}`

First, we need to find the midpoint of each interval:

The midpoint of interval = 1/2 (lower class limit + upper-class limit)

Then:

Time for competition (in minutes) ----- frequency ---- midpoint

9 -11 8 1/2(9+11) = 10

12 -14 7 1/2(12+14) = 13

15-17 5 1/2(15+17)= 16

18 - 20 3 1/2(18+20) = 19

21-23 3 1/2(21+23) = 22

Now, multiply the frequency of each interval by its midpoint:

10 * 8 = 80

13* 7 = 91

16 * 5 = 80

19 * 3 = 57

22 *3 = 66

Summ all the results 80 + 91 +80+57+66= 374

Then, sum all the frecuencys = 8 + 7 +5 +3 +3 = 26

Use the mean formula =

`Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}`
`Mean\text{ of a gruop data =}(374)/(26)=14.38461`

The mean is given using five decimals.