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# Statistics PowerPoint PPT Presentation

Statistics. Context Data Variation. 5 number summary. Max Min Median Q1 Q3 Range Mean Mode IQR Sum n. Write up. Write the data in sentences Write the explanation in paragraph format Context, use it before or after the explanation. CUSS- Center, Unusual, shape, spread.

Statistics

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## Statistics

Context

Data

Variation

• Max

• Min

• Median

• Q1

• Q3

• Range

• Mean

• Mode

• IQR

• Sum

• n

### Write up

• Write the data in sentences

• Write the explanation in paragraph format

• Context, use it before or after the explanation.

• CUSS- Center, Unusual, shape, spread.

### Pair up

• Find the mean, median, and mode of the following collection.

• 15, 11, 19, 15, 14, 13, 17, 11, 12, 17, 15, 14, 15

• 1. Find the mean, median, mode, and range of the following collection of scores on a test.

• 32, 72, 81, 95, 98, 58, 77, 75, 83, 97, 45, 89, 93, 57, 82, 97, 52, 75, 79, 78, 99, 98, 54, 75, 85, 61, 55, 86

• Find the first, second, and third quartiles of the collection of data in Exercise 1.

• 32, 72, 81, 95, 98, 58, 77, 75, 83, 97, 45, 89, 93, 57, 82, 97, 52, 75, 79, 78, 99, 98, 54, 75, 85, 61, 55, 86

• Construct a box-and-whisker plot of the collection of data

### With a partner

• Complete #1-3 for the following set of data. The weights (in pounds) of eleven children are as follows: 39, 52, 40, 45, 46, 55, 48, 40, 43, 47, 44

### Organizing Data

• At a car dealership, the number of new cars sold in a week by each salesperson was as follows: 5, 8, 2, 0, 2, 4, 7, 4, 1, 1, 2, 2, 0, 1, 2, 0, 1, 3, 3, 2

### a. Construct a frequency distribution for this data.

• 5, 8, 2, 0, 2, 4, 7, 4, 1, 1, 2, 2, 0, 1, 2, 0, 1, 3, 3, 2

• Number, Tally, Frequency

### Construct a line plot for this data

• 5, 8, 2, 0, 2, 4, 7, 4, 1, 1, 2, 2, 0, 1, 2, 0, 1, 3, 3, 2

### Construct a bar graph that shows the number of salespeople who sold 0-8 cars.

• 5, 8, 2, 0, 2, 4, 7, 4, 1, 1, 2, 2, 0, 1, 2, 0, 1, 3, 3, 2

### Construct a frequency distribution and a line plot for this data.

• Twenty-eight students in a class were asked how many cars their family owned. The results were as follows:

• 2, 2, 3, 2, 1, 2, 2, 4, 3, 2, 0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 3, 5, 1, 1, 3, 0, 1, 2

### Construct a bar graph that shows these results

• Each of the members of a recent high school graduating class was asked to name his/her favorite among these subjects: English, foreign language, history, mathematics, science. The results are shown in the table

• English 62

• Foreign Language 40

• History 40

• Mathematics 18

• Science 33

### Construct a stem-and-leaf plot for the unordered data

• 63, 52, 84, 83, 51, 32, 58, 35, 45, 41, 65, 75, 59, 67, 25, 46

• A stem-and-leaf plot orders data in increasing or decreasing order.

### Histograms

• 1.Construct and label a horizontal number line that is scaled to contain all of the values of the variable of interest.2. Construct and label a vertical axis so that the greatest frequency can be represented.

• 3. Construct the bars of equal width that are centered above each value. The heights of the bars represent the frequencies of the values.

### Construct a stem-and-leaf plot for the data

• 15, 59, 66, 42, 48, 23, 70, 81, 35, 51, 68, 29, 77, 92, 85, 16, 37, 59, 61, 76, 40, 25, 86, 11, 34, 52, 16, 22, 89, 55, 47, 39, 27, 42, 46, 51, 24, 69, 78, 91, 90, 65

### Construct a histogram for the above data.

• 15, 59, 66, 42, 48, 23, 70, 81, 35, 51, 68, 29, 77, 92, 85, 16, 37, 59, 61, 76, 40, 25, 86, 11, 34, 52, 16, 22, 89, 55, 47, 39, 27, 42, 46, 51, 24, 69, 78, 91, 90, 65

### Box plot and stem and leaf plot

• Graph a box plot for the following test scores: {90, 80, 96, 54, 80, 95, 100, 75, 87, 62, 65, 85, 92, 87, 74, 89}

• Draw a stem and leaf plot for the data

### Write up with Context

• Explain the shape in the context of the problem! For example, consider a distribution of grades which is skewed to the right and has a median score of 70. Do not write "The distribution is skewed to the right." Instead write "Many students had scores close to 70, but a few students scored much higher."

• The box in a boxplot represents the interquartile range and gives the interval which contains 50% of the observations. 25% of the observations are less than the first quartile, and 25% of the observations are greater than the third quartile.

at a school field day, 50 students and 50 faculty members each completed an obstacle course. Descriptive statistics for the completion times (in minutes) for the two groups are shown below:

• Use the same scale to draw boxplots for the completion times for students and for faculty members.

• (b)  Write a few sentences comparing the variability of the two distributions.

• (c)  You have been asked to report on this event for the school newspaper. Write a few sentences describing student and faculty performances in this competition for the paper.