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Summarizing Data Flashcards

Summarizing Data Flashcards
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A group of 5 cats has a mean whisker length of 12 inches. Find the whisker length of a 6th cat that would drop the mean to 11 inches.

12 inches * 5 cats = 60

(60 + x) / 6 = 11

66 = 60 + x

x = 6

The cat's whiskers would need to be 6 inches to bring the mean whisker length to 11 inches.

Got it
Spread in Data

A measure of how far from the middle of a data set the individual values are

Examples: range, interquartile range, and variance

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Interquartile Range

The difference between the 1st and 3rd quartiles of a data set

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Measures of Central Tendency

Measures that aim to describe the central value of a set of data

Three main types: mean, median, mode

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Find the mode of the height:

In increasing order: 68, 69, 70, 70, 71, 71, 72, 72, 72, 73, 74

Mode = most frequent number = 72

Got it
Find the range of the following data set: {100, 112, 120, 124, 131, 131, 108}

Range = largest value - smallest value = 131 - 100 = 31

Got it
Find the median of the following data set: {100, 112, 120, 124, 131, 131, 108}

In increasing order: 100, 108, 112, 120, 124, 131, 131

Median = number in middle = 120

Got it
Find the mean of the following data set: {100, 112, 120, 124, 131, 131, 108}

100 + 112 + 120 + 124 + 131 + 131 + 108 = 826 / 7 = 118

Got it
Find the mode of the following data set: {1, 2, 3, 4, 1, 2, 3, 1, 5, 7}

In increasing order: 1, 1, 1, 2, 2, 3, 3, 4, 5, 7

Mode = most frequent number = 1

Got it
Finding a student's percentile if they are in 4th place in a class of 20 people.

p = (k + 0.5r) / n

k = 16; r = 1; n = 20

p = (16 + 0.5x1) / 20 = 0.825 = 83rd percentile

Got it
Calculate the standard deviation for the following numbers to the nearest hundredth. {1, 3, 4, 2, 2}

1. Mean: 2.4

2. Data points - mean: -1.4, 0.6, 1.6, -0.4, -0.4

3. Squared: 1.96, 0.36, 2.56, 0.16, 0.16

4. Variance: 1.04

5. Square root: 1.02 = standard deviation

Got it
Calculate the standard deviation of the following numbers to the nearest hundredth. {4, 6, 8, 7, 5, 10}

1. Mean: 6.67

2. Data points - mean: -2.67, -0.67, 1.33, 0.33, -1.67, 3.33

3. Squared: 7.13, 0.45, 1.77, 0.11, 2.79, 11.09

4. Variance: 3.89

5. Square root: 1.97 = standard deviation

Got it
Calculate the mean of this data set to the nearest whole number: {99, 98, 97, 76, 85, 84, 80, 95, 74, 79, 70}

99 + 98 + 97 + 76 + 85 + 84 + 80 + 95 + 74 + 79 + 70 = 937 / 11 = 85

Got it
Calculate the mean of the following set of data: {12, 14, 15, 22, 13, 45, 8}

12+14+15+22+13+45+8 = 129/7=18

Got it

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Flashcard Content Overview

These flashcards will help you review the basic ways we summarize data. This includes looking at measures of center such as the mean, median, and mode, as well as measures of variation, like the standard deviation, range, and interquartile range. They also will help you review how these measures can change when looking at a sample of a population.

Front
Back
Calculate the mean of the following set of data: {12, 14, 15, 22, 13, 45, 8}

12+14+15+22+13+45+8 = 129/7=18

Calculate the mean of this data set to the nearest whole number: {99, 98, 97, 76, 85, 84, 80, 95, 74, 79, 70}

99 + 98 + 97 + 76 + 85 + 84 + 80 + 95 + 74 + 79 + 70 = 937 / 11 = 85

Calculate the standard deviation of the following numbers to the nearest hundredth. {4, 6, 8, 7, 5, 10}

1. Mean: 6.67

2. Data points - mean: -2.67, -0.67, 1.33, 0.33, -1.67, 3.33

3. Squared: 7.13, 0.45, 1.77, 0.11, 2.79, 11.09

4. Variance: 3.89

5. Square root: 1.97 = standard deviation

Calculate the standard deviation for the following numbers to the nearest hundredth. {1, 3, 4, 2, 2}

1. Mean: 2.4

2. Data points - mean: -1.4, 0.6, 1.6, -0.4, -0.4

3. Squared: 1.96, 0.36, 2.56, 0.16, 0.16

4. Variance: 1.04

5. Square root: 1.02 = standard deviation

Finding a student's percentile if they are in 4th place in a class of 20 people.

p = (k + 0.5r) / n

k = 16; r = 1; n = 20

p = (16 + 0.5x1) / 20 = 0.825 = 83rd percentile

Find the mode of the following data set: {1, 2, 3, 4, 1, 2, 3, 1, 5, 7}

In increasing order: 1, 1, 1, 2, 2, 3, 3, 4, 5, 7

Mode = most frequent number = 1

Find the mean of the following data set: {100, 112, 120, 124, 131, 131, 108}

100 + 112 + 120 + 124 + 131 + 131 + 108 = 826 / 7 = 118

Find the median of the following data set: {100, 112, 120, 124, 131, 131, 108}

In increasing order: 100, 108, 112, 120, 124, 131, 131

Median = number in middle = 120

Find the range of the following data set: {100, 112, 120, 124, 131, 131, 108}

Range = largest value - smallest value = 131 - 100 = 31

Find the mode of the height:

In increasing order: 68, 69, 70, 70, 71, 71, 72, 72, 72, 73, 74

Mode = most frequent number = 72

Measures of Central Tendency

Measures that aim to describe the central value of a set of data

Three main types: mean, median, mode

Interquartile Range

The difference between the 1st and 3rd quartiles of a data set

Spread in Data

A measure of how far from the middle of a data set the individual values are

Examples: range, interquartile range, and variance

A group of 5 cats has a mean whisker length of 12 inches. Find the whisker length of a 6th cat that would drop the mean to 11 inches.

12 inches * 5 cats = 60

(60 + x) / 6 = 11

66 = 60 + x

x = 6

The cat's whiskers would need to be 6 inches to bring the mean whisker length to 11 inches.

Find the mean and median for the following data set: {180, 185, 160, 175, 210, 210, 205}

In increasing order: 160, 175, 180, 185, 205, 210, 210

Mean: 160 + 175 + 180 + 185 + 205 + 210 + 210 = 1325 / 7 = 189.3

Median: 185

Using Mean vs. Median

Mean: useful for finding the central tendency of data that are close together

Median: useful when data includes outliers to prevent skewing the analysis

Find the mean and median, and determine which value is the better measure of central tendency for the following data set: {20, 22, 24, 25, 26, 27, 60}

Mean: 20 + 22 + 24 + 25 + 26 + 27 + 60 = 204 / 7 = 29

Median: 25

The median is more appropriate because of the outlier (60) skewing the mean to the right

Describe the distribution:

Bimodal non-symmetrical distribution

Find the standard deviation to the nearest hundredth for the following data set: {10, 10.5, 10.3, 11, 15, 20, 16.7}

1. Mean: 13.36

2. Data points - mean: -3.36, -2.86, -3.06, -2.36, 1.64, 6.64, 3.34

3. Squared: 11.29, 8.18, 9.36, 5.57, 2.69, 44.09, 11.16

4. Variance: 13.19

5. Square root: 3.63 = standard deviation

Find the standard deviation to the nearest hundredth for the following data set: {3, 3, 4, 4, 5}

1. Mean: 3.8

2. Data points - mean: -0.8, -0.8, 0.2, 0.2, 1.2

3. Squared: 0.64, 0.64, 0.04, 0.04, 1.44

4. Variance: 0.512

5. Square root: 0.72 = standard deviation

Find the mode of the following data set: 10, 14, 15, 12, 10, 14, 19, 12, 14

Arranged in increasing order: 10, 10, 12, 12, 14, 14, 14, 15, 19

Mode = 14

Simple Random Sample

A method of sampling in which every member has an equal chance (or probability) of being chosen

Determine if the following is a simple random sample: 10 students were chosen from a chemistry classroom to serve as a sample of the school

Not a simple random sample: not every student in the school had an equal chance of being selected

The Law of Large Numbers

States that larger sample sizes lead to the sample mean being closer to the mean of the population (a more accurate statistical representation of the population)

Sample Mean

The average of the data found from the sample

To calculate: add all data points together, then divide by the total number of data points

Standard Error

How close a sample mean is to the data expected from the population

To calculate: take the standard deviation of sample and divide by the square root of sample size

Quartile

The values that separate a data set into 4 groups

2nd quartile: the median of the data

1st quartile: the median of the first half of the data

3rd quartile: the median of the second half of the data

Find the interquartile range for the following data set: {70, 68, 84, 85, 82, 81, 90, 92, 94, 72}

In increasing order: 68, 70, 72, 81, 82, 84, 85, 90, 92, 94

Median (quartile 2): 83

Median of 1st half (quartile 1): 72

Median of 2nd half (quartile 3): 90

90-72 = 18

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