Sections B-C Measures of Center and Spread

Measures of Center and Spread

Sections B/C -- Thursday September 3, 2026

Categorize

Options (7)

Your cell phone number

Name of your favorite movie

Number of people attending Trenton Thunder baseball game

Seating capacity of football stadium

Number of red cars in the MCCC west student parking lot

The amount of time you wait to see a doctor

The amount of electricity used by a household during a given month

Homework Review (#5):
Organize these variables into the right categories

Qualitative

Quantitative Discrete

Quantitative Continuous

Multiple Choice

Which of the following is NOT a common measure of central tendency?

• Mode

• Median

• Mean

• Range

Open Ended

Professors were observed wearing the number of colored shirts shown in the table on the first day of classes. Find the "average" of this distribution and state what the "average" means (if anything) in this context. Also state which measure of central tendency it is.

(HW #6)

Multiple Choice

We will use Frequency tables often when we are analyzing categorical (qualitative) data. In the frequency table, you (or your calculator) have already done the work of counting.
What is the mode of this distribution?

(Ex 3, p9)

• Vanilla

• Chocolate

• Strawberry

• 10

Dropdown

The median is the data value in the ​

Select answer

of a sorted data set. The data set may not contain a data element equal to the median if there are a(n) ​

Select answer

number of entries in the distribution.

Multiple Choice

What is the median of: 45 47 52 54 58 63 65 67 73 75 79?

• 54

• 58

• 63

• 65

Multiple Choice

What is the median of: 56 59 62 64 65 67 68 69 70 74?

• 64

• 65

• 66

• 67

Multiple Choice

When should you use the mean instead of the median to describe a data set?

• When the data are skewed

• When the data are not skewed and are quantitative

• When there are outliers

• When the data are categorical

Match

Match the distribution's skew to the relationship between the mean and the median.

• Left (negatively) skewed

• Right (positively) skewed

• Symmetric (bell-shaped)

mean is less than the median

mean is greater than the median

Mean generally equals the median

• mean is less than the median

• mean is greater than the median

• Mean generally equals the median

Multiple Choice

The standard deviation of the sample is just the square root of the sample's variance (s² ).
Which part of the standard deviation formula represents the mean (average) of all the scores?

• $$x$$

• $$\overline{x}$$

• $$\sum_{ }^{ }\left(x-\overline{x}\right)^2$$

• $$n-1$$

Open Ended

Why is the $$\left(x-\overline{x}\right)$$ term squared before it is summed? (Hint: what is the sum of the distance from the mean)?

Match

You can use the "computational formula" for the sample standard deviation (instead of using the calculator).
For the following set of numbers, match the statistic to its value.

{10 12 14 17 18 20}

(Ex 1, p12)

• n

• Σx

• Σx²

• s²

• s

6

91

1453

14.57

3.82

• 6

• 91

• 1453

• 14.57

• 3.82

Match

Using your calculator, match the statistic to its value based on this distribution:
A: {15 16 25 29 32 39 41 48 46 47}

(Ex 3, p13)

• n

• Σx

• Σx²

• s²

• s

10

338

12802

153.07

12.37

• 10

• 338

• 12802

• 153.07

• 12.37

Match

After adding 20 to each of the values of the previous distribution {A}, match the statistic to its value based on this new distribution:
A₊₂₀ : {35 36 45 49 52 59 61 68 66 67}

• $$\overline{x}=\sum_{ }^{ }x\div n$$

• $$s^2$$

• $$s$$

53.8

153.07

12.37

• 53.8

• 153.07

• 12.37

Match

After multiplying each of the values of the previous distribution {A} by 12, match the statistic to its value based on this new distribution:
A_x12: {180 192 300 348 384 468 492 576 552 564}

• $$\overline{x}=\sum_{ }^{ }x\div n$$

• $$s^2$$

• $$s$$

• $$\frac{12\left(338\right)}{10}$$

• $$12^2\left(153.07\right)$$

• $$12\left(12.37\right)$$

Match

IQ scores are approximately bell-shaped with a mean of 100 and a standard deviation of 15. Match the following IQ score values to their percentages.

(Ex 1, p14)

• $$70$$

• $$130$$

• $$85\le x\le115$$

• $$55\le x\le145$$

Low barrier for 95% of IQ scores

High barrier for 95% of IQ scores

68%

99.7%

• Low barrier for 95% of IQ scores

• High barrier for 95% of IQ scores

• 68%

• 99.7%

Categorize

Options (17)

Mean

Median

Range

Variance

Standard Deviation

Interquartile Range

Mode

μ

σ²

σ

P

N

$$\overline{x}$$  

$$s^2$$  

$$s$$  

$$n$$  

$$p$$  

Categorize the following parameters or statistics into their most common usage

Measure of Central Tendency

Measure of Spread

Population Parameters

Sample Statistics