week 8

Question 1

Front

Answer 1

Back

Question 2

Definition: Median

Answer 2

The median is the middle value of a sorted dataset. If n is even, it’s the average of the two middle values.

Question 3

Definition: Mean

Answer 3

The mean (average) is (\bar{x} = \frac{1}{n}\sum x_i). Add all values, then divide by the number of observations.

Question 4

Formula: Variance

Answer 4

Sample variance is (s^2 = \frac{\sum(x_i - \bar{x})^2}{n - 1}). It’s the average squared deviation from the mean (with n-1 in the denominator).

Question 5

Formula: Standard Deviation (SD)

Answer 5

Standard Deviation = (s = \sqrt{ s^2 }). It returns the spread measure to the original data units.

Question 6

Formula: Interquartile Range (IQR)

Answer 6

IQR = Q3 – Q1, the distance between the 75th and 25th percentiles.

Question 7

Definition: Outlier (Boxplot)

Answer 7

A data point is often labeled an outlier if it’s beyond 1.5 × IQR above Q3 or below Q1.

Question 8

Formula: z-score

Answer 8

(z = \frac{x - \bar{x}}{s}). Indicates how many SDs above (+) or below (–) the mean a point is.

Question 9

Definition: Histogram

Answer 9

A histogram is a bar chart for quantitative data, grouping data values into equal-width bins.

Question 10

Steps: Boxplot Construction

Answer 10

1) Determine 5-number summary (min, Q1, median, Q3, max). 2) Draw box from Q1 to Q3. 3) Mark median. 4) Calculate fences at 1.5 × IQR. 5) Draw whiskers to data within fences; mark outliers beyond them.

Question 11

Formula: Coefficient of Variation (CV)

Answer 11

(CV = \frac{s}{\bar{x}} \times 100\%). Measures relative spread compared to the mean.

Question 12

Definition: Correlation Coefficient (r)

Answer 12

r = from –1 to +1, measuring linear relationship strength between two numeric variables.

Question 13

Formula: Percentile Location

Answer 13

For the p-th percentile in n data points: (i = \frac{p}{100}(n+1)). If i isn’t integer, interpolate.