BUS250

Seminar 4

• Mean: the arithmetic average of a set of data or sum of the values divided by the number of values.

• Median: the middle value of a data set when the values are arranged in order of size.

• Mode: the value or values that occur most frequently in a data set.

Key Terms

Find the mean of a data set1. Find the sum of the values.

2. Divide the sum by the total number of values.

Mean = sum of values

number of values

Try these examples

• Mileage for the new salesperson has been 243, 567, 766, 422 and 352 this week. What is the average number of miles traveled?

• 470 miles daily

• Prices from different suppliers of 500 sheets of copier paper are as follows: $3.99, $4.75, $3.75 and $4.25. What is the average price?

• $4.19

7.1.2 Find the Median• Arrange the values in the data set from smallest

to largest (or largest to smallest) and select the value in the middle.

• If the number of values is odd, it will be exactly in the middle.

• If the number of values is even, identify the two middle values. Add them together and divide by two.

Here is an example• A recent survey of the used car market for the particular

model John was looking for yielded several different prices: $9,400, $11,200, $5,900, $10,000, $4,700, $8,900, $7,800 and $9,200. Find the median price.

• Arrange from highest to lowest:$11,200, $10,000, $9,400, $9,200, $8,900, $7,800, $5,900 and $4,700.

• Calculate the average of the two middle values.

• (9,200 + 8,900) ÷ 2 = $9,050 or the median price

Look at this example

78 84 95 88 99 92 87 94 90 77 Class Class RelativeInterval Frequency Calculations Frequency 75-79 2 2/10 20% 80-84 1 1/10 10% 85-89 2 2/10 20% 90-94 3 3/10 30% 95-99 2 2/10 20% Total 10 10/10 100%

Here’s an example

Local Daycare Market Share

43%

35%

16%

6%

Teddy Bear

La La Land

Little Gems

Other

Key Terms

• Measures of central tendency: statistical measurements such as the mean, median or mode that indicate how data groups toward the center.

• Measures of variation or dispersion: statistical measurement such as the range and standard deviation that indicate how data is dispersed or spread.

• Range: the difference between the highest and lowest values in a data set. (also called the spread)

• Deviation from the mean: the difference between a value of a data set and the mean.

• Standard variation: a statistical measurement that shows how data is spread above and below the mean.

Key Terms

• Variance: a statistical measurement that is the average of the squared deviations of data from the mean. The square root of the variance is the standard deviation.

• Square root: the quotient of number which is the product of that number multiplied by itself. The square root of 81 is 9. (9 x 9 = 81)

• Normal distribution: a characteristic of many data sets that shows that data graphs into a bell-shaped curve around the mean.

Key Terms

7.3.1 Find the Range in a Data Set

• Find the highest and lowest values.

• Find the difference between the two.

• Example: The grades on the last exam were 78, 99, 87, 84, 60, 77, 80, 88, 92, and 94.

The highest value is 99.

The lowest value is 60.

The difference or the range is 39.

7.3.2 Find the Standard Deviation

• The deviation from the mean of a data value is the difference between the value and the mean.

• Get a clearer picture of the data set by examining how much each data point differs or deviates from the mean.

Deviations from the mean

• When the value is smaller than the mean, the difference is represented by a negative number indicating it is below or less than the mean.

• Conversely, if the value is greater than the mean, the difference is represented by a positive number indicating it is above or greater than the mean.

Find the deviation from the mean

• Find the mean of a set of data.

• Mean = Sum of data values

Number of values

• Find the amount that each data value deviates or is different from the mean.

• Deviation from the mean = Data value - Mean

Here’s an example

• Data set: 38, 43, 45, 44

• Mean = 42.5

• 1st value: 38 – 42.5 = -4.5 below the mean

• 2nd value: 43 – 42.5 = 0.5 above the mean

• 3rd value: 45 – 42.5 = 2.5 above the mean

• 4th value: 44 – 42.5 = 1.5 above the mean

Find the standard deviation of a set of data

• A statistical measure called the standard deviation uses the square of each deviation from the mean.

• The square of a negative value is always positive.

• The squared deviations are averaged (mean) and the result is called the variance.

• The square root is taken of the variance so that the result can be interpreted within the context of the problem.

• This formula averages the values by dividing by one less than the number of values (n-1).

• Several calculations are necessary and are best organized in a table.

Find the standard deviation of a set of data

1. Find the mean.

2. Find the deviation of each value from the mean.

3. Square each deviation.

4. Find the sum of the squared deviations.

5. Divide the sum of the squared deviations by one less than the number of values in the data set. This amount is called the variance.

6. Find the standard deviation by taking the square root of the variance.

Find the standard deviation of a set of data

Find the standard deviationFind the standard deviation for the following

data set: 18 22 29 27 Deviation Squares ofValue Mean from Mean Deviation 18 24 18 – 24 = -6 -6 x -6 = 36 22 24 22 – 24 = -2 -2 x -2 = 4 29 24 29 – 24 = 5 5 x 5 = 25 27 24 27 – 24 = 3 3 x 3 = 9

Sum of Squared Deviations 74

Variance = sum of squared deviations

n – 1

Variance = 74 ÷ 3 = 24.666667

Standard deviation = square root of the variance

Standard deviation = 4.97 rounded

Find the standard deviation of a set of data