Business Mathematics Chapter 22 Statistics

Calculate the mean: $1,001, $68.50, $33.82, $581.95.

$1,001 + $68.50 + $33.82 + $581.95 = $1,685.27 $1,685.27 / 4 = $421.3175 Mean = $421.32

Intervals can be used with bar graphs.

True

9.1% of a circle graph represents

.091 × 360° = 32.76°

How many degrees on a circle graph would each be given from the following? Wear digital watch 42 % Wear traditional watch 51 % Wear no watch 7 %

.42 x 360 = 151.20 degrees .51 x 360 = 183.60 degrees .07 x 360 = 25.20 degrees

Angie's Bakery bakes bagels. The June production is given below. 200 150 200 150 200 150 190 360 360 150 190 190 190 200 150 360 400 400 150 200 400 360 150 400 360 400 400 200 150 150 Find the weighted mean.

150 bagels x 9 days = 1,350 190 bagels x 4 days = 760 200 bagels x 6 days = 1,200 360 bagels x 5 days = 1,800 400 bagels x 6 days = 2,400 9 + 4 + 6 + 5 + 6 = 30 days (Frequency) 1350 + 760 + 1200+ 1800 + 2400 = 7,510 Weighted mean = 7,510 / 30 = 250.33

What is the weighted mean frequency for the following car sales? 2 sold at $25,090 3 sold at $20,000 1 sold at $21,475 1 sold at $39,638

2 x $25,090 = $50,180 3 x $20,000 = $60,000 1 x $21,475 = $21,475 1 x $39,638 = $39,638 $171,293/7 = $24,470

Match the graph type to its purpose/definition

Bar Graph: Shows changes over time Circle Graph: Shows the relationship of parts to a whole Line Graph: Shows trends over a period of time

BAR GRAPHS

Bar graphs help readers see the changes that have occurred over a period of time. This is especially true when the same type of data is repeatedly studied. Note that the height of the bar represents the frequency of each purchase. Bar graphs can be vertical or horizontal.

Assume the mean useful life of a particular light bulb is 2,000 hours and is normally distributed with a standard deviation of 300 hours. Calculate the useful life of the light bulb within two standard deviations of the mean.

Because it is within 2 standard deviations: 2000 - 600 = 1400 2000 + 600 = 2600 Between 1,400 and 2,600 hours.

All means should be rounded to the nearest tenth.

False

The median is the middle value for an even number of values.

False - The median is the middle value for an odd number of values.

In a bar graph, the height of the bar indicates the ____ of the value.

Frequency

From the following numbers, the median is: 16, 9, 10, 5, 4

In Order: 4, 5 , 9 , 10, 16 The middle number = 9

EMPIRICAL RULE

In a normal distribution, the mean, median, and mode are all equal. Additionally, when the data are normally distributed, the Empirical Rule (Three Sigma Rule) applies, stating that for a normal distribution, also known as a bell curve, approximately: 68% of the observations will fall within ± 1 standard deviation of the mean, 95% will fall within ± 2 standard deviations of the mean, and 99.7% will fall within ± 3 standard deviations of the mean.

In a normal distribution, data are spread symmetrically around the:

Mean

Sales of CD's during the week are as follows: 14,17, 20, 24, and 25 Find the sales of CD's one standard deviation from the mean.

Mean = 14+ 17+ 20 + 24 + 25 = 100 / 5 = 20 Mean ± standard deviation. 20 - 4.6 = 15.4 20 + 4.6 = 24.6 Therefore, data within one standard deviation is 15.4 to 24.6

Match the term/terms to the definitions.

Measure of Dispersion: Describes how numbers in a data set are spread out. Mean, Median, and Mode: Identify a single value to represent a group of numbers

Match the best average method used for the stated high/low numbers/

Median: High/low numbers ARE affected Mean: High/low numbers are NOT affected

Which statement about line graphs is FALSE?

Only one trend can be drawn

The range of 105, 100, 79, 86, 101, 94, 98, 87, and 83 is:

Ordered = 79, 83, 86, 87, 94, 98, 100, 105 105 - 79 = 26

Find the median: 95, 103, 98, 62, 31, 15, 82

Organized: 15, 31, 62, 82, 95, 98, 103 Middle Value = 82

Last year a company sold entertainment consoles for $299. This year they sell for $349. What is the price relative of the entertainment console?

Price Relative = Current Year Price / Base Year Price x 100 349 / 299 x 100 = 117%

A business math class consisted of five students ages 17, 17, 36, 38, and 44. What is the class range?

Range = Highest Value - Lowest Value 44 - 17 = 27

RANGE

Range is the difference between the two extreme values (highest and lowest) in a group of values or a set of data. Range = Highest Value - Lowest Value

Measures of dispersion are:

Range, Standard Deviation, and normal distribution

Use the following table: $ 210 $ 505 $ 310 $ 380 $ 275 290 480 550 490 200 286 410 305 444 368 Prepare a frequency distribution from the above weekly salaries of teachers at Moore Community College. Use the following intervals:

Salaries Frequency 200 - $299.99 5 300 - 399.99 4 400 - 499.99 4 500 - 599.99 2

FINDING THE STANDARD DEVIATION

Standard Deviation is intended to measure the spread of data around the mean, you must first determine the mean of a set of data. Step 1. Find the mean of the set of data. Step 2. Subtract the mean from each piece of data to find each deviation. Step 3. Square each deviation (multiply the deviation by itself). Step 4. Sum all squared deviations. Step 5. Divide the sum of the squared deviations by n − 1, where n equals the number of pieces of data. Step 6. Find the square root (√) of the number obtained in Step 5 (use a calculator). This is the standard deviation. (The square root is a number that when multiplied by itself equals the amount shown inside the square root symbol.)

FINDING THE MEDIAN OF A GROUP OF VALUES

Step 1. Orderly arrange values from the smallest to the largest. Step 2. Find the middle value. A. Odd number of values: Median is the middle value. You find this by first dividing the total number of numbers by 2. The next-higher number is the median. B. Even number of values: Median is the average of the two middle values.

WEIGHTED MEAN

Sum of Products / Sum of Frequencies

MEAN

Sum of all values / number of values Add all the values together and divide by the number of values added. Example: Sales of CD's during the week were as follows: 14, 17, 20, 24, and 25 14 + 17 + 20 + 24 + 25 = 100 / 5 = 20

Alvin's Bakery produced the following number of oat bran muffins each week: Week 1 : 700 Week 2: 700 Week 3: 600 Week 4: 500 Week 5: 700 Week 6: 600 In a frequency distribution, which would have the lowest tally?

The number 500 appears once.

Frequency of occurrence is used in finding the weighted mean.

True

Use the following table: Computer Principles 3 Credits B Grade Business Law 3 Credits C Grade Logic 3 Credits D Grade Biology 4 Credits A Grade Marketing 3 Credits B Grade A = 4, B = 3, C = 2, D = 1, F = 0 Calculate the grade-point average.

Weighted Mean = Sum of Products / Sum of Frequencies 2.69

In a bar graph, the grouping or intervals should be of _____ Sizes.

equal

Select the denominator in the standard deviation formula.

n - 1; where n = the number of data pieces.

MODE

the value that occurs most often is the mode EXAMPLE: 3, 4, 5, 6, 3, 8, 9, 3, 5, 3 3 is the mode since it is listed 4 times.

Find the mode: 22, 19, 15, 16, 18, 18, 5, 18

the value that occurs most often is the mode Mode = 18