# Standard Deviation Problems

### Solutions

1Find the standard deviation for the following data series:

12, 6, 7, 3, 15, 10, 18, 5.

2Find the standard deviation for the following series of numbers:

2, 3, 6, 8, 11.

12, 6, 7, 3, 15, 10, 18, 5.

3Find the standard deviation for the series:

3, 5, 2, 7, 6, 4, 9.

3, 5, 2, 7, 6, 4, 9, 1.

4Given the statistical distribution of the table.

 xi 61 64 67 70 73 fi 5 18 42 27 8

Calculate the standard deviation.

5A statistical distribution is given by the following table:

 [10, 15) [15, 20) [20, 25) [25, 30) [30, 35) fi 3 5 7 4 2

Calculate the standard deviation.

6The heights of the players (in centimeters) from a basketball team are represented by the table:

 Height [170, 175) [175, 180) [180, 185) [185, 190) [190, 195) [195, 2.00) No. of players 1 3 4 8 5 2

Calculate:

1. The standard deviation.

2. How many players are above the mean plus one standard deviation?

7Given the absolute cumulative frequency table:

 Age Fi [0, 2) 4 [2, 4) 11 [4, 6) 24 [6, 8) 34 [8, 10) 40

Calculate the standard deviation.

## 1

Find the standard deviation for the following data series:

12, 6, 7, 3, 15, 10, 18, 5.   ## 2

Find the standard deviation for the following series of numbers:

2, 3, 6, 8, 11.  #### Standard Deviation 12, 6, 7, 3, 15, 10, 18, 5.  #### Standard Deviation ## 3

Find the standard deviation for the series:

3, 5, 2, 7, 6, 4, 9.  #### Standard Deviation 3, 5, 2, 7, 6, 4, 9, 1.  #### Standard Deviation ## 4

Given the statistical distribution of the table.

 xi 61 64 67 70 73 fi 5 18 42 27 8

Calculate standard deviation.

 xi fi xi · fi xi2 · fi 61 5 305 18 065 64 18 1152 73 728 67 42 2814 188 538 71 27 1890 132 300 73 8 584 42 632 100 6745 455 803  #### Standard Deviation ## 5

A statistical distribution is given by the following table:

 [10, 15) [15, 20) [20, 25) [25, 30) [30, 35) fi 3 5 7 4 2

Calculate the standard deviation.

 xi fi xi · fi xi2 · fi [10, 15) 12.5 3 37.5 468.75 [15, 20) 17.5 5 87.5 1537.3 [20, 25) 22.5 7 157.5 3543.8 [25, 30) 27.5 4 110 3025 [30, 35) 32.5 2 65 2112.5 21 457.5 10681.25  #### Standard Deviation ## 6

The heights of the players (in centimeters) from a basketball team are represented by the table:

 Height [170, 175) [175, 180) [180, 185) [185, 190) [190, 195) [195, 2.00) No. of players 1 3 4 8 5 2

Calculate:

3. The standard deviation.

4. How many players are above the mean plus one standard deviation?

 xi fi Fi xi · fi xi2 · fi [1.70, 1.75) 1.725 1 1 1.725 2.976 [1.75, 1.80) 1.775 3 4 5.325 9.453 [1.80, 1.85) 1.825 4 8 7.3 13.324 [1.85, 1.90) 1.875 8 16 15 28.128 [1.90, 1.95) 1.925 5 21 9.625 18.53 [1.95, 2.00) 1.975 2 23 3.95 7.802 23 42.925 80.213 #### 1 #### 2

x + σ = 1.866+ 0.077 = 1.943

This value belongs to a percentile that is in the penultimate interval.  There are only 3 players above x + σ.

## 7

Given the absolute cumulative frequency table:

 Edad Fi [0, 2) 4 [2, 4) 11 [4, 6) 24 [6, 8) 34 [8, 10) 40

1. Calculate the arithmetic mean and standard deviation.

2. Calculate the difference between the values that are the 10 central ages?

3. Create the respective absolute cumulative frequency polygon.

 xi fi Fi xi · fi xi2 · fi [0, 2) 1 4 4 4 4 [2, 4) 3 7 11 21 63 [4, 6) 5 13 24 65 325 [6, 8) 7 10 34 70 490 [8, 10) 9 6 40 54 486 40 214 1368  