S2 Research methods - 1

Central Tendency

A value representing the typical average or central value in a dataset, including mean, median, and mode.

Normal Distribution

A symmetrical, unimodal distribution where mean, median, and mode are at the center, with specific percentages of scores falling within certain standard deviations.

Z Scores

Standardized scores with a mean of 0 and a standard deviation of 1, used to compare individual scores to a distribution.

Mean

The sum of all data points divided by the number of observations in a dataset.

Median

The middle data value when data is arranged in ascending or descending order.

Mode

The data value that occurs with the highest frequency in a dataset.

advantages of mean

• uses all values

• is sensitive

advantage of median

• not affected by outliers

advantages of mode

• the only measure that can be used for categorical data

disadvantage of the mean

• outliers can affect the mean

disadvantages of median

• doesnt not use all data

• not very sensitive

disadvantages of mode

• possible to have more than one mode or no mode - not useful

Standard Normal Distribution

A type of normal distribution with a mean of zero and a standard deviation of one.

Z Score Calculation

Formula to calculate a Z score:Z = (X - M) / SD, where X is the individual score, M is the mean, and SD is the standard deviation.

Raw Score Calculation

Formula to find a raw score from a Z score:X = M + Z*SD, where X is the raw score, M is the mean, Z is the Z score, and SD is the standard deviation.

Z Score Significance

A Z score of 1.96 marks the top 2.5% and -1.96 marks the bottom 2.5% of a distribution, with 95% of scores falling between them.

z scores are…

standardised scores a group of data points transformed to have a mean of 0 and a SD of 1 like the normal distribution

𝘟−𝝻/𝞂 means

individual score - mean score/ standard deviation

a Z score of 1.96 is the cutt off for…

the top 2.5% of the distribution

a Z score of -1.96 is the cuttoff for

the bottom 2.5% of the distribution

X = 𝝻 + Z𝞂 what does X mean?

raw score, individual score or test results

X = 𝝻 + Z𝞂. what does 𝝻 mean?

the mean

X = 𝝻 + Z𝞂. what does Z mean?

Z score

X = 𝝻 + Z𝞂 .what does 𝞂 mean?

the standard deviation

the distribution of scores on a stats test has a mean of 60 and a standard deviation of 20. what is the Z score of a score of 70?

0.5

the distribution of scores on a stats test has a mean of 80 and a SD of 20 if their Z score was 0.5 what was their test score?

90

three people take 3 different but equivalent tests of intelligence which is the highest relative score (Z score)

1. score of 144 with a mean of 128 and SD of 34

2. score of 90 with a mean of 86 and a standard deviation of 18

3. a score of 18 on a test with a mean of 15 and a standard deviation of 5

1. 0.4706

2. 0.2222

3. 0.6

3 wins

if jimmy has a Z score of 2.6 what percentage of the other test takers has it beaten

99.53%

jimmys annoying brother got a Z score of -0.27 what percentage of test takers did better or worse than him

jimmys brother is better than 39.36% and worse than 60.64%

if you eat more biscuits than 96% of the biscuit eating population whats ur Z score?

0.96 critical value - 1.751