Exercise 19 Page 312

There are four steps to follow when finding the standard deviation of a set of data.

1. Find the mean of the data.
2. Find the squared deviation of each data value.
3. Find the mean of the squared deviations.
4. Find the square root of the mean of the squared deviations.

Let's start by finding the mean, or average, of the data set from the exercise.

Mean=Sum of values/Number of values

SubstituteValues

Substitute values

Mean=279.11+271.04+309.73+363.38+409.72+444.74+603.46+695.39+871.96+972.35/10

AddTerms

Add terms

Mean=5220.88/10

CalcQuot

Calculate quotient

Mean=522.088

RoundDec

Round to 2 decimal place(s)

Mean=522.09

The mean is $522.09. Now, we can find the deviation from the mean for each value and square it. Let's use a table to organize the information.

Data Value	Deviation from Mean	Squared Deviation	Round to whole number
279.11	279.11-522.09= -242.98	( -242.98)^2 = 59039.28	59039
271.04	271.04-522.09= -251.05	( -251.05)^2=63026.102	63026
309.73	309.73-522.09= -212.36	( -212.36)^2=45096.769	45097
363.38	363.38-522.09= -158.71	( -158.71)^2 = 25188.864	25189
409.72	409.72-522.09= -112.37	( -112.37)^2=12627.016	12627
444.74	444.74-522.09= -77.35	( -77.35)^2=5983.0225	5983
603.46	603.46-522.09= 81.37	( 81.37)^2=6621.0769	6621
695.39	695.39-522.09= 173.30	( 173.30)^2=30032.89	30033
871.96	871.96-522.09= 349.87	( 349.87)^2=122409.01	122409
972.35	972.35-522.09= 450.26	( 450.26)^2=202734.06	202734

Next, we can find the mean of the squared deviations.

59039+63026+45097+25189+12627+5983+6621+30033+122409+202734/10

AddTerms

Add terms

572758/10

CalcQuot

Calculate quotient

57275.8

The final step is to find the square root of the mean of the squared deviations. sqrt(57275.8) ≈ 239.3 The standard deviation of the data is approximately $239.30.