The first step in finding the mode, mean and median is to write the scores in order from smallest to largest.

45 48 51 54 55 56 58 60 67 72 73 75 76 77 80 81 82 83 84 88 90 90 91 95 98

MEDIAN The median is the middle number of a data set when the numbers are arranged in numerical order. If there is no middle number, the median is the mean of the

two middle numbers. In this case, the median of the scores is 76.

Test Scores: 90, 95, 60, 80, 75, 83, 54, 91, 77, 56, 58, 90, 76, 98, 84, 48, 72, 82, 51, 88, 45, 67,

73, 81, 55

MODE The mode is the data value or values that occur most frequently in a data set.

There may be no mode for a data set. The mode for the test scores is 90.

MEAN

The mean is computed by adding the individual scores and dividing that sum by the total number of test scores.

90+95+60+…+81+55=1,829= 𝟏,𝟖𝟐𝟗𝟐𝟓 = 𝟕𝟑. 𝟏𝟔 = 𝟕𝟑.𝟐

Ms. Rios’ 25 students took a probability math test. Their test scores were written on the board:

Add the squared differences & divide by the number of test

scores, 25. 5,976.425

= 𝟐𝟑𝟗.𝟏

TEST SCORES

X

SUBTRACT THE MEAN, 73.2 FROM EACH TEST SCORE

X-x ̄

SQUARE EACH DIFFERENCE. ROUND

ONE DECIMAL PLACE. (X-x ̄)2

45 -28.2 795.2 48 -25.2 635.0 51 -22.2 492.8 54 -19.2 368.6 55 -18.2 331.2 56 -17.2 295.8 58 -15.2 231.0 60 -13.2 174.2 67 -6.2 38.4 72 -1.2 1.4 73 -0.2 0 75 1.8 3.2 76 2.8 7.8 77 3.8 14.4 80 6.8 46.2 81 7.8 60.8 82 8.8 77.4 83 9.8 96.0 84 10.8 116.6 88 14.8 219.0 90 16.8 282.2 90 16.8 282.2 91 17.8 316.8 95 21.8 475.2 98 24.8 615.0

VARIANCE The variance is the number found by subtracting the mean from each data

value, squaring each of these differences, finding the sum of these squares, and then dividing by the total number of data values in the set.

STANDARD DEVIATION The standard deviation is the square root of the variance. In this case, take the

square root of the variance, 239.1 to find the standard deviation. √239.1 = 15.46285 = 𝟏𝟓.𝟓

1st STANDARD DEVIATION 68% The two numbers that are on the right and left from the mean 73.2

57.7 &88.7

2nd STANDARD DEVIATION 95% The number on the left of 57.7 and on the right of 88.7

42.2 &104.2

3rd STANDARD DEVIATION 99.7% The numbers sitting under the bell curve

26.7 &119.7