Math

QuestionA dice is rolled 100 times. Find the range, mode, and median from the frequencies: 16, 25, 17, 19, 8, 15. Also, estimate the mean time from: 2, 8, 12, 16, 12 in intervals (10-20, 20-25, 25-30, 30-50, 50-80).

Studdy Solution

STEP 1

Assumptions1. The dice is fair and each face has an equal chance of appearing. . The rolls are independent, meaning the result of one roll does not affect the result of another.
3. The frequencies given in the table are correct and complete.

STEP 2

(i) To find the range, we need to subtract the smallest score from the largest score.
Range=LargestscoreSmallestscoreRange = Largest\, score - Smallest\, score

STEP 3

Plug in the values for the largest and smallest scores to calculate the range.
Range=61Range =6 -1

STEP 4

Calculate the range.
Range=61=Range =6 -1 =

STEP 5

(ii) The mode is the score with the highest frequency. Looking at the table, we can see that the score with the highest frequency is2.

STEP 6

(iii) To find the median, we first need to find the middle score. Since the dice was rolled100 times, the middle score is the average of the50th and51st scores when the scores are arranged in numerical order.

STEP 7

Looking at the cumulative frequency, we can see that the50th and51st scores both fall within the frequency of the score4.

STEP 8

Therefore, the median score is4.

STEP 9

(d) To estimate the mean time taken by the students, we first need to find the midpoint of each time interval.

STEP 10

The midpoints are calculated as followsMidpoint=Lowerlimit+Upperlimit2Midpoint = \frac{{Lower\, limit + Upper\, limit}}{2}

STEP 11

Calculate the midpoints for each time interval.

STEP 12

Multiply each midpoint by its corresponding frequency to get the total time for each interval.

STEP 13

Add up all the total times to get the total time taken by all students.

STEP 14

Divide the total time by the total number of students (50) to get the estimated mean time.
Meantime=Totaltime50Mean\, time = \frac{{Total\, time}}{50}

STEP 15

Calculate the mean time.
The range is5, the mode is2, the median is4, and the estimated mean time is calculated in step15.

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