Lecture 4 Flashcards by Alexander Lee

What are descriptive statistics?

Methods for organizing and summarizing data

example: table or graph

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A descriptive value for a population is called a __________

parameter

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a descriptive value for a sample is called a ___________

statistic

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What does the Mu symbol represent?

The mean for a population

NOT a sample

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Frequency Distribution vs Grouped Frequency Distribution

Frequency distribution- presents organized picture of entire set of scores

Grouped frequency distribution- Some statistics are grouped together to accomadate for a wider range of scores

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If the scores in a population are measured on an interval/ratio scale and the N is large…. the data will present as a ___________

smooth curve instead of a jagged histogram

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T or F: a smooth curve shows the exact frequency of every score

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Describe a normal distribution

symmetrical bell shape

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What is a skew of frequency distribution?

Nonsymmetrical distribution of data

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What kind of skew is this?

Positive skew

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What kind of skew is this?

Negative skew

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What is Kurtosis of a graph?

The “peakedness” of the distribution

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Leptokurtic vs Platykurtic

Describe the Kurtosis of a graph

Leptokurtic = High, thin peak

Platykurtic = lower/broader peak

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How does a stem and leaf distribution work?

Each score divided into stem and leaf

the stem contains the first digit(s) and the leaf contains the final digits

example: 3//3582 represents the scores 33 35 38 32

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What are 3 measures of central tendency?

Mode Median and Mean

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Bimodal vs Multimodal

Having 2 modes vs having multiple modes

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Mode definition

Most frequently occuring number

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What kind of data is appropriate for using a Mode?

All types: Nominal, Ordinal, Interval, and Ratio

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Median definition

If the scores are listed smallest to largest, it is the midpoint of the list

If odd numbers, it’s the middle number

if even numbers, its the average of the middle 2 numbers.

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What kind of data is appropriate for use of the median

Ordinal Interval and Ratio data

NOT nominal

What is one advantage of using the Median?

It is relatively unaffected by extreme scores

The Mean can be used as a representation of central tendency for what kind of data?

Interval and Ratio

NOT Nominal or Ordinal

When should we not report the mean?

When there are extreme scores that will pull the mean in one direction

When you’re using a nominal scale

In a central distrubtion, the mean and median will ____________

Always be equal and always be in the middle

(mean, median, mode) In a skew, what stays in the middle of the curve? What is skewed most towards the tail? What is in the middle?

Mode Mean Median

Descriptive statistic vs inferential statistic in variability:

A **descriptive statistic** measures the *degree to which scores are spread out* **Inferential statistic** measures how *accurately* an *individual score or sample represents an entire population*

A _______ variability means scores will more liekly give a good view of the whole population

Low

How to measure range for this set? 4, 5, 7, 8, 9, 11

11- 4 = 7

How to calculate standard deviation for a sample?

1. First calculate the variance of every score from the mean. Each score - the mean 2. Square all of those numbers and add them together 3. Divide by N - 1 if it's for a sample, just N if it's for a population 4. Take the square root of the answer

what does n-1 represent when calculating standard deviaton?

Degrees of freedom

On a normal distribution __% of scores will be 1 standard deviation from the mean

70%

On a normal distribution __% of scores will be 2 standard deviations from the mean

On a normal distribution __% of scores will be 3 standard deviations from the mean

What does a Z score tell you?

Gives you context of how a score relates to other scores in the distribution

How to calculate a Z score?

(Score - Mean) / Standard Deviation = Z score note: Z score will always be a really small number

What are inferential statistics?

Methods for using sample data to make general conclusions about a population using probability Rather than just describing the data like descriptive statistics

When graphed on a normal distribution, probability can be defined as the ____________________ the curve

the portion under the curve

Are Z scores for populations or samples?

Populations, not samples

How to use a Z score table?

You can use a coresponding Z score to find the **probability** that something will *fall into the body vs the tail of the graph*

Z scores will only work if the data has a _______ distribution

normal

If you sample _____ people you will end up with a normal distribution

What is the central limit theorem?

As sample size increase it approaches a normal distribution 30 will have a more normal distribution than 15

T or F: population data can be any size or any shape, but if you have a sample of 30+ it will be very close to normal distribution

What is SEM (Standard Error of the Mean)

Difference between Sample Mean and True Population mean

What is the difference between SEM and SD?

**Standard Deviation** compares the amount of variability of a set of data, from the mean **SEM**- measures how far the sample mean is likely to be from the population mean **SEM is ALWAYS smaller than SD**

How do you calculate SEM? SD of sample: 5 Sample size: 50

50/ SqRt(5) The smaller the number = less sampling error likely

What is a point estimate vs an interval estimate?

These are ways to use estimates to represent a population **Point estimate**- using the mean of your sample **Interval estimate**- using a span of numbers that includes the mean

What is a confidence interval/interval estimate

Range of numbers inferred from the sample that has a known probability of capturing the true population parameter Example: AVG GPA = 3.4 with a 95% confidence interval that it's between 3.2 and 3.6