Math

QuestionFind the mode, median, mean, and range of the following percentages: 60, 84, 82, 66, 96, 60, 90, 64, 66, 76.

Studdy Solution

STEP 1

Assumptions1. The percentage marks of all students are given in the table. . The modal percentage mark is the one that occurs most frequently.
3. The median is the middle value when the data is arranged in ascending order.
4. The mean or average is the sum of all values divided by the number of values.
5. The range is the difference between the highest and lowest values.

STEP 2

To find the modal percentage mark, we need to identify the percentage mark that appears most frequently in the data set.
The given percentages are60,84,82,66,96,60,90,64,66,76.

STEP 3

From the given data, we can see that the percentage mark60 and66 appear twice, and all the other marks appear only once. So, the modes are60 and66.

STEP 4

To find the median, we first need to arrange the data in ascending order.
The arranged data is60,60,64,66,66,76,82,84,90,96.

STEP 5

Since there are10 data points, an even number, the median is the average of the5th andth data points.
Median=(5thdatapoint+thdatapoint)/2Median = (5th\, data\, point +th\, data\, point) /2

STEP 6

Plug in the values for the5th and6th data points to calculate the median.
Median=(66+76)/2Median = (66 +76) /2

STEP 7

Calculate the median.
Median=(66+76)/2=71Median = (66 +76) /2 =71

STEP 8

To find the mean, we need to sum all the percentage marks and divide by the total number of students.
Mean=(Sumofallpercentagemarks)/(Numberofstudents)Mean = (Sum\, of\, all\, percentage\, marks) / (Number\, of\, students)

STEP 9

Sum all the percentage marks and divide by the total number of students.
Mean=(60+84+82+66+96+60+90+64+66+76)/Mean = (60 +84 +82 +66 +96 +60 +90 +64 +66 +76) /

STEP 10

Calculate the mean.
Mean=(60+84+82+66+96+60+90+64+66+76)/10=74.4Mean = (60 +84 +82 +66 +96 +60 +90 +64 +66 +76) /10 =74.4

STEP 11

To find the range, we need to subtract the smallest percentage mark from the largest percentage mark.
Range=LargestpercentagemarkSmallestpercentagemarkRange = Largest\, percentage\, mark - Smallest\, percentage\, mark

STEP 12

Plug in the values for the largest and smallest percentage marks to calculate the range.
Range=9660Range =96 -60

STEP 13

Calculate the range.
Range=9660=36Range =96 -60 =36The modal percentage marks are60 and66, the median is71, the mean is74., and the range is36.

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