Statistics

Question 1

Name Frequency distributions

Answer 1

Frequency Counts and Percentages

Question 2

Name measures of Central Tendency

Answer 2

Mean
Median
Mode

Question 3

Name measures of Variability

Answer 3

Range
Variance
Standard Deviation
Interquartile Range

Question 4

___ tally the number of times each category appears, offering a straightforward way to identify the most and least common categories

Answer 4

Frequency counts (n) tally the number of times each category appears, offering a straightforward way to identify the most and least common categories

Question 5

__ represent frequency counts as a part of the whole and can help in comparing the relative sizes of different categories, making it easier to interpret the data across groups of varying sizes.

Answer 5

Percentages (%) represent frequency counts as a part of the whole and can help in comparing the relative sizes of different categories, making it easier to interpret the data across groups of varying sizes.

Question 6

What is the purpose of frequency distributions?

Answer 6

Purpose: Identify initial patterns, imbalances, and the most/least common responses in a dataset

Question 7

Average, Sum of all numbers ➗# of numbers (skewed by outlier)

Answer 7

Mean

Question 8

Middle. Rank order & middle number (not skewed by outlier)

Answer 8

Median

Question 9

Most common & used with nominal data set (not skewed by outlier)

Answer 9

Mode

Question 10

Interpretive relationships:

Mean < Median < Mode = __ skewed
Mode < Median < Mean = __ skewed
Mean = Median = Mode →___ skewed

Answer 10

Mean < Median < Mode = negatively skewed (right)
Mode < Median < Mean = positively skewed (left)
Mean = Median = Mode → symmetric (normal) distribution

Question 11

Purpose of measures of central tendency

Answer 11

Measures of Central Tendency: typical value in the dataset/interpreting the dataset

Question 12

Purpose of Measures of Vairability

Answer 12

Measures of Variability: describe overall spread & reliability of data

Question 13

Difference between the highest and lowest value; Max - Min =

Answer 13

Range: Difference between the highest and lowest value; Max - Min = Range.
Greater Range = wider spread.

Question 14

___ average of the squared differences from the mean ↑= more spread out

Answer 14

Variance: average of the squared differences from the mean ↑= more spread out

Question 15

__ Square root of the variance, providing a measure of dispersion that is in the same units as the data. average distance of each data point from the mean.

Answer 15

Standard Deviation: Square root of the variance, providing a measure of dispersion that is in the same units as the data. average distance of each data point from the mean.
* Larger SD = Greater variability
* Smaller SD = data is more tightly clustered
* Mean ↔ Standard Deviation
Variance = 250 √250 = 15.8 = SD

Question 16

___ spread of the middle half of a dataset, range between the 25th and 75th percentile. Median ↔___

Answer 16

Interquartile Range: spread of the middle half of a dataset, range between the 25th and 75th percentile. Median ↔ IQR
* variability of the data around the median, giving us a clearer picture of where most of the data lies.
* Ex: 60,70,80,90,100 = 70 - 90 = IQR

Question 17

____ make predictions or inferences about a larger population based on sample data. Draw conclusions & make predictions

Answer 17

Inferential Statistics: make predictions or inferences about a larger population based on sample data. Draw conclusions & make predictions

Question 18

The Normal Distribution

Answer 18

Bell shaped curve, symmetrical distribution aka unimodal
Mean = Median = Mode are all equal
* Must have Normal distribution to use empirical rule

Question 19

___ describes how data are distributed in a normal distribution

Answer 19

The Empirical Rule: describes how data are distributed in a normal distribution

Question 20

What is the Emprical rule

Answer 20

The Empirical Rule: describes how data are distributed in a normal distribution
Normal distribution only
When a distribution is normally distributed, the Empirical Rule states that:
* 68% of the observations fall within ± 1 standard deviation of the mean
* 95% fall within ± 2 standard deviation of the mean
* 99.7% fall within ± 3 standard deviation of the mean

Allows researchers to estimate how typical or unusual a value is
Helps identify outliers or abnormal values

Question 21

___ as sample size increases, the distribution of sample means becomes normally distributed

Answer 21

Central Limit Theorem: as sample size increases, the distribution of sample means becomes normally distributed
* If you take enough averages from a group, those averages will form a bell-shaped curve (normal distribution), even if the original group wasn’t bell-shaped.

Question 22

Key Points

1) The mean of the sampling distribution is the mean of the _____.
2) The standard deviation of a sampling distribution is called the ___ ____ ___ ___ ___ .
3) The sampling distribution follows a ___ distribution, allowing use of the __ ___

Answer 22

1) The mean of the sampling distribution is the mean of the population.
2) The standard deviation of a sampling distribution is called the standard error of the mean.
3) The sampling distribution follows a normal distribution, allowing use of the empirical rule

Question 23

What is confidence interval? 

Answer 23

Confidence interval provides a range of values that is believed with a stated level of confidence to contain the true population parameter (most often the population mean)

Question 25

True or false A 95% confidence interval means there is a 95% probability that the population mean is inside one specific interval. 

Answer 25

**FALSE** A 95% confidence interval gives us a range of values that we believe with considerable certainty include the true population value. * It does not mean there is a 95% probability that the population mean is inside one specific interval.