# Summarizing Data Flashcards

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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.

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

Examples: range, interquartile range, variance, and standard deviation

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

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

Three main types: mean, median, mode

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

Mode = most frequent number = 72

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

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

Median = number in middle = 120

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

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

Mode = most frequent number = 1

*p* = (*k* + 0.5*r*) / *n*

*k* = 16; *r* = 1; *n* = 20

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

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: 1.0 = standard deviation

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

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

Numbers ordered from smallest to largest: 8, 12, 13, 14, 15, 22, 45

Median = number in the middle = 14

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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.

Numbers ordered from smallest to largest: 8, 12, 13, 14, 15, 22, 45

Median = number in the middle = 14

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

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

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: 1.0 = standard deviation

*p* = (*k* + 0.5*r*) / *n*

*k* = 16; *r* = 1; *n* = 20

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

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

Mode = most frequent number = 1

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

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

Median = number in middle = 120

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

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

Mode = most frequent number = 72

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

Three main types: mean, median, mode

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

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

Examples: range, interquartile range, variance, and standard deviation

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.

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

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

Median: 185

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

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

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

Median: 25

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

Bimodal non-symmetrical distribution

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: 3.6 = standard deviation

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: 0.56

5. Square root: 0.75 = standard deviation

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

Mode = most frequent number = 14

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

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

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)

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

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

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

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

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

You can find this by adding up all the numbers in a data set and then dividing that sum by the total number of initial figures.

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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

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- Overview of Statistics Flashcards
- Summarizing Data Flashcards
- Probability Flashcards
- Discrete Probability Distributions Flashcards
- Continuous Probability Distributions Flashcards
- Regression & Correlation Flashcards
- Statistical Estimation Flashcards
- Hypothesis Testing in Statistics Flashcards
- Z-Scores & Standard Normal Curve Areas Statistical Table
- Critical Values of the t-Distribution Statistical Table
- Binomial Probabilities Statistical Tables
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