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Interquartile Range

In statistics, the interquartile range refers to the overall difference between the higher quartile value of a data set and the accompanying lower quartile value. A data set can be split up into three quartiles when you consider the whole set of values to be out of 100%. This is how the three quartiles can be defined: Q1 = this is the first quartile and represents the first 25% of the data, also known as the 25th percentile. Q2 = this is the second quartile and represents the median of the data, also known as the 50th percentile. Q3 = this is the third quartile and represents the first 75% of the data, also known as the 75th percentile. To find the interquartile range, the first quartile needs to be subtracted from the third quartile. Therefore, the formula is: Q3- Q1 = interquartile range. For example, you are given a data set in which Q1 = 22.3, Q2 = 40.8 and Q3 = 65.3. What is the interquartile range? = Q3 – Q1 = 65.3 – 22.3 = 43 Additionally, the interquartile range can be determined from a box plot. In a box plot, quartiles are marked on the figure directly and so, when analyzing a box plot, the values for Q1 and Q3 can be identified, and thus, the interquartile range can be derived. By obtaining the interquartile range, the amount of variation which exists around the median can be interpreted. Therefore, just like other quantitative measures, the interquartile range represents another method of describing a data set.

Range, Interquartile Range, Variance, Standard Deviation

The Los Angeles Times regularly reports the air quality index for various areas of Southern california. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50. 1. Compute the range and interquartile range. 2. Compute the sample variance and sample standard deviat

Percentile rank and inter-quartile range: Example question

For a normally distributed test with a mean of 100 and standard deviation of 20: a) What score would be associated with the 80th percentile? b) What would the inter-quartile range be for the test? c) What would be the percentile rank of a score of 125? Please give detailed notes explaining the steps required to answer ea

Statistics Interquartile Range

Carl and Angela both work at a computer store. Each salesperson recorded the number of computers sold each month for a year. Box-and-whisker plots representing the number of computers sold per month are shown at the right. a. What is the interquartile range of Carl's sales? b. What is the

Summary, Interquartile Range, and Outliers

The following data shows the waiting times in minutes for the customers in a bank before the customer is served. Waiting times: 0.38 2.34 3.02 3.20 3.54 3.79 4.21 4.50 4.77 5.12 5.13 5.55 6.10 6.19 6.46 a) Write the five number summary (the minimum, Q1, Median, Q2, and the maximum.) b) What is