Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.

Short Answer

Expert verified

The standard deviation tells us the variability of the data.

Step by step solution

01

Standard deviation

The variance or standard deviation of how much variance as well as dispersion there is in a group of numbers.A smaller standard deviation suggests that information is grouped around the mean, whereas a largestandard deviation showsthat observations are more dispersed.

02

Explaining the preference of standard Deviation over the range

The range is the difference between the maximum and the minimum value of the data set.It allows you to know the gap between the data set.

Standard Deviation tells us how far a particular value is from the data set's mean. It tells us how far the data is spread from the mean.

We generally prefer standard Deviation over the range because it allows us to understand the data set's variability. In contrast, the range only tells us the difference between the maximum and the minimum value.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Question: For a set of data with a mound-shaped relative frequency distribution, what can be said about the percentage of the measurements contained in each of the intervals specified in Exercise 2.72?

Parking at a university has become a problem. The university’s administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 190 students and recorded how long it took each of them to find a parking spot. The durations had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 190 times collected.

Treating psoriasis with the “Doctorfish of Kangal.”Psoriasis is a skin disorder with no known cure and noproven effective pharmacological treatment. An alternative treatment for psoriasis is ichthyotherapy, also known as therapy with the “Doctorfish of Kangal.” Fish from the hot pools of Kangal, Turkey, feed on the skin scales of bathers, reportedly reducing the symptoms of psoriasis. In one study, 67 patients diagnosed with psoriasis underwent 3 weeks of ichthyotherapy (Evidence-Based Research in Complementary and Alternative Medicine,December 2006). The Psoriasis Area Severity Index (PASI) of each patient was measured both before and after treatment. (The lower the PASI score, the better is the skin condition.) Box plots of the PASI scores, both before (baseline) and after 3 weeks of ichthyotherapy treatment, are shown in the accompanying diagram.

a.Find the approximate 25th percentile, the median, and the 75th percentile for the PASI scores before treatment.

b.Find the approximate 25th percentile, the median, and the 75th percentile for the PASI scores after treatment.

c.Comment on the effectiveness of ichthyotherapy in treating psoriasis.

Question: Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.47 (p. 96). Recall that slices of sandstone blocks were tested for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C). Measures of variation for the permeability measurements (mV) of each sandstone group are displayed in the accompanying Minitab printout.

Descriptive Statistics: PermA, PermB, PermC

Variable

N

StDev.

Variance

Minimum

Maximum

Range

PermA

100

14.48

209.53

55.20

122.40

67.20

PermB

100

21.97

482.75

50.40

150.00

99.60

PermC

100

20.05

401.94

52.20

129.00

76.80

a.Find the range of the permeability measurements for Group A sandstone slices. Verify its value using the minimum and maximum values shown on the printout.

b.Find the standard deviation of the permeability measurements for Group A sandstone slices. Verify its value using the variance shown on the printout.

c.Which condition (A, B, or C) has the more variable permeability data?

Question: Construct a scatterplot for the data in the following table.

Variable 1: 5 1 1.5 2 2.5 3 3.5 4 4.5 5

Variable 2: 2 1 3 4 6 10 9 12 17 17

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free