Chapter 3 Statistics Part 3

Midquartile

(Q3+Q1)/2

semi-interquartile range

(Q3-Q1)/2

Converting from the kth percentile to the corresponding data value (solving steps)

1) Sort the data. Arrange the data in order from lowest to highest 2) Compute L= (k/100)*n n= number of values k= percentile in question 3) is L a whole number? No?-> change L by rounding it up to the next larger whole number. The value of Pk is the Lth value counting from the lowest. Yes?->The value of the Kth percentile is midway between the Lth value and the next value in the sorted set of data. Find Pk by adding the Lth value and the next value and dividing total by 2

Boxplot - Construction

1.Find the 5-number summary. 2.Construct a scale with values that include the minimum and maximum data values. 3.Construct a box (rectangle) extending from Q1 to Q3 and draw a line in the box at the value of Q2 (median). 4.Draw lines extending outward from the box to the minimum and maximum values. Divide sorted data values into 4 equal parts 25%, 25%, 25%, 25% Minimum and maximum value on both ends with Q1,2, and 3 in the middle Do not draw box plot, just write the 5 number summary

5-Number Summary Consists of...

1.Minimum value 2.First quartile Q1 3.Second quartile Q2(same as median) 4.Third quartile, Q3 5.Maximum value

Converting from the kth percentile to the corresponding data value (Equation)

L= k/100 * n n= total number of data values in the data set k= percentile being used L= locator that gives the position of a value Pk= kth percentile i.e P40= ? Step 1: 40/100 * number of values =L Step 2: L= Whole Number? Whole number + (Whole number +1)/2 L= Not a whole number? Roundup i.e if it was 6.7 I would round to the 7th location (round up to the location)

10-90 percentile range

P90 - P10

Percentile Equation

Percentile of Value X= Number of Values Less than X/ (Total number of values) * 100

Interquartile Range

Q3-Q1

Quartiles

are measures of location, denoted Q1, Q2, and Q3, which divide a set of data into four groups with about 25% of the values in each group. Q1(First quartile) separates the bottom 25% of sorted values from the top 75%. Q2(Second quartile) same as the median; separates the bottom 50% of sorted values from the top 50%. Q3(Third quartile) separates the bottom 75% of sorted values from the top 25%.

Boxplot

is a graph of a data set that consists of: - a line extending from the minimum value to the maximum value - a box with lines drawn at the first quartile, Q1, the median, and the third quartile, Q3.

Percentiles

measures of location. There are 99 percentiles denoted P1, P2, . . ., P99, which divide a set of data into 100 groups with about 1% of the values in each group.