Question

and Statistics Project 1 A study was done to explore the number of chocolate bars consumed by 16-year-old girls in a month's time. The results are shown below Chocolate Bars 56 46 12 62 39 24 59 51 52 41 10 32 14 63 52 26

Answer 1

1. The level of measurement used in the study is Continuous (also called Scale)

2. Using SPSS,

View Data Transform Analyze Direct Marketing Graphs Utilities Add-ons Window Reports Descriptive Statistics Tables Compare Means General Linear Model Generalized Linear Models Mixed Models Correlate Regression Loglinear Neural Networks Classify Dimension Reduction 123 Frequencies Descriptives .. Ch bars consumed 乓Explore 56 46 12 62 39 24 59 51 39 52 Crosstabs... Ratio... P-P Plots Q-Q Plots...

Ch_bars_consumed var var varvar var var 56 46 12 62 303 24 59 51 39 52 28 41 10 64 Frequencies Variable(s) Statistics... Charts.. Format.. Bootstrap Ch bars consumed Display frequency tables OK Paste Reset Cancel Help

Ch bars consumed var var var 56 46 12 62 39 24 59 51 39 52 28 41 10 64 27 Frequencies: Statistics Percentile Values Central Tenden Mean Median Mode Sum Quartiles Cut points for: 10equal groups Percentile(s): Add Change Remove Values are group midpoints Display frequ Dispersion Distribution M.Std.deviatiori Minimum Maximum S.E. mean Variance Range Skewness Kurtosis 34 Continue Cancel Help 32

The output is obtained as:

Statistics Ch_bars_consumed 30 Missing Mean Median Mode Std. Deviation Variance 37.70 40.00 52 19.955 398.217

2.a. The mean , median and mode for the given data is obtained as 37.7,40 and 52 respectively.

2.b. The variance and Standard deviation is obtained as 398.217 and 19.955 respectively.

3.

a Transform Analyze Direct Marketing Graphs Utili Compute Variable.. Count Values within Cases Shift Value... Recode into Same Variables... Recode into Different Variables.. Automatic Recode... Visual Binning.. co Optial Binning... Prepare Data for Modeling Rank Cases Date and Time Wizard Create Time Series.. Replace Missing Values Random Number Generators Run Pending Transforms 64 Ctrl+G

Ch bars consumed var var 56 46 12 62 39 24 59 51 39 52 28 41 10 64 27 Visual Binning Select the variables whose values will be grouped into bins Data will be scanned when you click Continue The Variables list below contains all numeric ordinal and scale variables Variables Variables to Bin: Ch bars consumed 34 Limit number of cases scanned to Continue Cancel Help 32

Ch bars consumed Visual Binning 56 46 12 62 39 24 59 51 39 52 28 41 10 64 27 Scanned Variable List: Name Label: Ch bars.consumed Curent ariablehbars consumed Current Variable: Ch bars consumed Binned Variable: Chocolates Minimum: 0 Ch barsconsumed (Binned) Nonmissing Values Maximum: 64 7.11 14.22 21.33 28.44 35.56 42.67 49.78 56.89 64.00 71.11 Enter interval cutpoints or click Make Cutpoints for automatic intervals. A cutpoint value of 10, for example, defines an interval starting above the previous interval and ending Upper Endpoints () Included (仁) OExcluded () Make Cutpoints... Grid: at 10 Value Label Cases Scanned: 30 11.01 11 22.0 12- 22 33.023-33 44.0 34-44 Missing Values: 0 Copy Bins 4 34 From Another Variable HIGH 45+ Make Labels To Other Variables Reverse scale 32 42 24 OK Paste Reset Cancel Help

Click on 'Make Cutpoints.Cut points are computed as (No. of intervals - 1) and width is obtained by dividing the range (0 - 64) by no. of intervals and rounding the figure to the nearest whole no.

Make Cutpoints Ch bars consumed var OEqual Width Intervals 46 12 62 39 24 59 Intervals-fill in at least two fields First Cutpoint Location: Number of Cutpoints: 5 Width: Last Cutpoint Location: 44 Scanned Variable Ch_bars_co Equal Percentiles Based on Scanned Cases 39 52 28 41 10 Intervals -fill in either field Number of Cutpoints Width(%): 64.00 71.11 s. A cutpoint val erval and endin Upper Endpoir Cases Scanned O Included ( Missing Values Cutpoints at Mean and Selected Standard Deviations Based on Scanned Cases Excluded ( Make Cutpoints Make Labels Reverse sca H-1 Std. Deviation Copy Bins +-2 Std. Deviation From Another V +3 Std. Deviation To Other Varia Apply will replace the current cutpoint definitions with this specification. A final interval will include all remaining values: N cutpoints produce N+1 intervals 42 24 Apply Cancel Help

The output is obtained as:

.

Ch_bars_consumed 56 46 12 62 39 24 59 51 39 52 Atit 45+ 12 -22 45+ 34-44 23-33 Atit 45+ 34-44 5+ 23-33 34-44 1-11 45+ 23-33 4 41 10 27 34 34-44

Now, to create the grouped frequency table,

Data Transform Analyze Direct Marketing Graphs Utilities Add-ons Windo Reports Descriptive Statistics Tables Compare Means General Linear Model Generalized Linear Models Mixed Models Correlate Regression Loglinear 123 Frequencies... Descriptives.. 乓Explore bars consumed 56 46 12 62 39 24 59 Crosstabs.. Ratio... P-P Plots... Q-Q Plots

Ch bars consumed Chocolates var var var var var 45+ 45+ 12 - 22 45+ 34 - 44 23 -33 45+ 45+ 34 - 44 45+ 23 -33 34- 44 1-11 45+ 23 -33 46 12 62 39 24 59 Frequencies Variable(s): Statistics... Charts Format. Bootstrap... Ch bars consumed Ch bars consume... 39 52 28 41 10 64 Display frequency tables OK Paste Reset Cancel Help 34 34 - 44

Ch bars_consumed (Binned) Cumulative Percent Frequency Percent Valid Percent 3.3 10.0 6.7 20.0 16.7 43.3 100.0 3.3 10.0 6.7 20.0 16.7 43.3 100.0 3.3 13.3 20.0 40.0 56.7 100.0 1-11 12- 22 23-33 34- 44 13 Total 30

4. To construct a histogram:

View Data Transform Analyze Direct Marketing Graphs Utilities Add-ons Window Help Chart Builder Graphboard Template Chooser... Legacy Dialogs Bar.. Ch bars consumed Chocolates var 3-D Ba.. 56 46 12 62 39 24 59 51 39 52 28 45+ 45+ 12 - 22 45+ 34- 44 23 -33 45+ 45+ 34- 44 45+ 23 - 33 34 - 44 1.11 Line... Area... Pie High-Low Boxplot.. Error Bar... Population Pyramid... Scatter/Do.. Histogram...

Ch bars consumed Chocolates var Histogram 56 46 12 62 39 24 59 51 39 52 28 41 10 64 27 45+ 45+ 12 -22 45+ 34 - 44 23 - 33 45+ 45+ 34 - 44 45+ 23 -33 34 - 44 1-11 45+ 23 -33 Variable Titles Ch_ bars_consumedC Ch_bars_consumed (Binned)... Display normal curve Panel RowS Nest variables (no empty rows) Columns Nest variables (no empty columns) Template 34 - 44 1-11 45+ 23 - 33 34 - 44 23-33 34 Use chart specifications from: File OK Paste |Reset Cancel Help 32 42

We get the output as:

12.5 10.0 CO 5 7.5 5.0 2.5 Ch bars_consumed (Binned)

where the X axis denotes the 6 bins of the grouped frequency table.