Descriptive statistics pt II

Question 1

Practice drawing frequency table questions.

Answer 1

get 80% score

Question 2

Practice arithmetic mean questions.

Answer 2

Get 80% score

Question 3

What does Σ stand for?

in statistical and calculus formulae

and what does the i at the bottom stand for?

Answer 3

The Greek letter capital sigma (Σ) indicates summation.

The “i = 1” at the bottom indicates that the summation is to start with X1

Question 4

Geometric mean

Recall geometric mean

and its formula

Answer 4

(G.M) of a series containing n observations is the nth root of the product of all the values.

(x1x2 x3* x4* x5*…xn)^(1/n)

Question 5

Example of geometric mean question and application. Let’s say you own a piece of art that increases in value by 50% the first year after you buy it, 20% the second year, and 90% the third year.

To answer, write equation you will use and answer

Answer 5

(1.5* 1.2* 1.9)(1/3) = 1.50663725458

Question 6

Q2 of geometric mean. The average person’s monthly salary in a certain town jumped from $2,500 to $5,000 over the course of ten years. Using the geometric mean, what is the average yearly increase?

Answer 6

1. Find the geometric mean. (2500*5000)^(1/2) = 3535.53390593.
2. Divide by 10

since it asks 10 years

final ans: 353.53

Question 7

What are the steps in obtaining harmonic mean?

e.g. 1, 5, 8, 10

https://www.statisticshowto.com/calculus-definitions/harmonic-mean/

Answer 7

1. Get reciprocals of the data
2. Add reciprocals
3. get mean of reciprocals
4. reciprocate answer

1/1 + 1/5 + 1/8 + 1/10 = 1.425 then (1.425/4)^-1

2.80702

Question 8

Median

What are the steps to obtain median?

Answer 8

1. Arrange in ascending order
2. If even divide middle numbers by 2

Question 9

Quartiles

How is data divided into quartiles?

Answer 9

1. Data is arranged in ascending order or in graph
2. divide total frequency by 4
3. at n/4 is each quartile

Question 9

Quartiles

How is data divided into quartiles?

Answer 9

1. Data is arranged in ascending order or in graph
2. obtain median which will be Q2 (2nd quartile line)
3. then on the divided data obtain median of each to obain Q1 and Q3

Question 10

Interquartile range

What is the interquartile range

Answer 10

It is the distance between the first and third quartile marks.

Q3-Q1

it tells us the range of the middle half of the data.

Question 11

Outliers

When is a point considered an outlier

Answer 11

When it is substantially above Q3 or below Q1

Question 12

How are outliers obtained?

Answer 12

1. 1.5*IQR then
2. add to Q3 or
3. minus from Q1

Question 13

Mode

What does mode refer to?

Answer 13

It refers to the value represented by the greatest number of individuals.

Question 14

Where is mode on the frequency distribution graph?

Answer 14

It is the value at which the curve peaks

Question 15

Distributions having two peaks (equal or unequal in height) are called?

Answer 15

Bimodal

Any more then they become multimodal

Question 16

Range

Define range as used in statistics.

Answer 16

the difference between the largest and the smallest values in a sample.

Question 17

What is one disadvantage if using range as a measure of dispersion?

Answer 17

it is extremely sensitive to outliers

Question 18

Variability

Variability can be defined as

Answer 18

how close the scores in a distribution are to the centre/mean.

Thus, one can see on average how far each data point is from the centre

Question 19

Measure of variability

One measure of variability is sum of squares. Write down the formula.

Answer 19

(SS) = ∑(X−μ)^2).

we square to get rid of negative values.

Note that as you calculate

Question 20

Variance

Variance is defined as the average squared difference of the scores from the mean. True or false?

Answer 20

True

Question 21

What is the symbol for variance

Answer 21

σ2 “sigma-squared”

Question 22

What is the formula for obtaining variance?

Answer 22

σ2=∑(X−μ)2/N-1

Basically, SS/N-1

N-1: is the degrees of freedom

Question 23

In general, as your sample size (N) gets bigger, the effect of subtracting 1 becomes less and less. What does this infer

Answer 23

larger sample sizes will bring the estimate of the sample variance closer to that of the population variance

Thus, larger sample sizes better reflect the population

Question 24

Standard deviation. σ

Standard deviation is

Answer 24

square root of the variance

most commonly used measure of spread

Question 25

The greater the standard deviation

in terms of distribution

Answer 25

the greater the distribution away from centre/mean.