# Univariate Statistics Case Example and Explanations – (CCJ4700 – Intro to research methods in criminology)

June 22, 2021 2021-06-22 13:49## Univariate Statistics Case Example and Explanations – (CCJ4700 – Intro to research methods in criminology)

# Univariate Statistics Case Example and Explanations – (CCJ4700 – Intro to research methods in criminology)

## Univariate Statistics

Univariate analysis is done on a singular variable with the goal of understanding the characteristics of the variable. First, univariate reveals the basic nature of the data such as its normal distribution, angled to the left or the right, outliers and related characteristics; these are gotten using tests such as normality test, t-test, and chi-square test. Second, it offers a descriptive view of the data including size of concentration, distribution patterns, among others. Third, univariate analysis helps in generating frequencies that can offer insight on specific portions of the data including group frequencies and characteristics. Some of the descriptive statistics explored under univariate analysis include mean, median, mode, minimum, maximum, skewness, standard deviation, kurtosis, among others.

As in Table 1, the mean for total crime arrest rate per 100,000 is 1779.0231. This implies that on average, 1779.0231 arrests are made per 100,000 people. The median is 1711.0783 which represents the midpoint of the dataset. The data is for 226 cities so the median is the point at the middle of the crime arrest data – or the average of the two values at the middle (113 and114). The mode is 0 which means that not single arrest rate occurs more frequently across the cities. The standard deviation (SD) is 1070.27592. The SD value shows that arrest rate values are dispersed from the mean Height (1779.0231) by over 1,070% which indicates that most of the arrest rate values are highly dispersed from the mean. The skewness is 0.550 which implies that the arrest rate data is mirrored, that is, neither skewed to the left or right. This is since the closer to 0 a skewness value is, the more the data is mirrored on both sides. The kurtosis value is 0.412 which indicates that the arrest rate data is close enough to being normally distributed. Normal distribution has a kurtosis value of 0 and hence 0.412 shows a slight positive kurtosis which translates to the arrest rate data curve having tails and peak comparable to the normal curve. The minimum value is 0 suggesting the least crime arrest rate among the cities is 0 people while the maximum value is 5112.07 indicating the highest crime arrest rate is 5112.07.

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Table 1 indicates the mean of murder offense rate per 100,000 as 8.8628. The interpretation is that the average murder offence rate for the cities is 8.8 people. The median 6.0702 which implies that this is the murder offence rate in the middle for the cities’ murder offence rate data set – or the average of the two values in the middle (113 and 114). Table 1 also shows mode as 0 which implies that there is no single repetitive murder offense rate The SD value is 9.31445 which suggests that there is an 9.31% dispersion of murder offence rate data from the mean murder offence rate (8.8628). The SD values thus indicates most values are closer to the mean. The skewness value is 2.341 which suggests that the data is not evenly mirrored between positive and negative planes; it is positively skewed. This is as the value (2.341) is not close to 0 . The kurtosis value is 7.795 which also implies positive distribution as opposed to normal distribution. The murder offence rate data thus peaks higher than normal distribution and has heavier tails. The minimum value – 0 – means the least murder offence rate for the cities is 0 pounds while the maximum value – 65.21– indicates the highest murder offence rate is 65.21 people.

The mean for death penalty status is 0.9027. The death penalty status was measured using a dummy variable with “0” being not a death penalty state and “1” being a death penalty state. There was a total of 226 cities. The mean value thus shows that 90.27% of the cities were in a death penalty state. And consequently 9.73 of the cities were in a no death penalty state.

In table 1, the mean for west region is 0.38. The west region values were also measured using a dummy variable. The value “0” represented cities not in the west and the value “1” represented cities in the west. The mean of 0.38 thus indicates that 38% of the cities were in the west. This also means that 62% of the cities were not in the west.

**Table 1: Univariate statistics**

Mean | Median | Mode | SD | Skewness | Kurtosis | Min | Max | |

total crime arrest rate per 100,000 | 1779.0231 | 1711.0783 | 0 | 1070.27592 | 0.550 | 0.412 | 0 | 5112.07 |

murder offense rate per 100,000 | 8.8628 | 6.0702 | 0 | 9.31445 | 2.341 | 7.795 | 0 | 65.21 |

death penalty status | 0.9027 | |||||||

west region | 0.38 |

**SPSS Content**

*SPSS syntax*

FREQUENCIES VARIABLES = atotind omurder deathpen west

/STATISTICS = MEAN MEDIAN MODE SKEWNESS KURTOSIS STDDEV MINIMUM MAXIMUM

*SPSS output*

Statistics | |||||

total crime arrest rate per 100,000 | murder offense rate per 100,000 | death penalty status | west region | ||

N | Valid | 226 | 226 | 226 | 226 |

Missing | 0 | 0 | 0 | 0 | |

Mean | 1779.0231 | 8.8628 | .9027 | .38 | |

Median | 1711.0783 | 6.0702 | 1.0000 | .00 | |

Mode | .00 | .00 | 1.00 | 0 | |

Std. Deviation | 1070.27592 | 9.31445 | .29709 | .487 | |

Skewness | .550 | 2.341 | -2.735 | .495 | |

Kurtosis | .412 | 7.795 | 5.529 | -1.770 | |

Minimum | .00 | .00 | .00 | 0 | |

Maximum | 5112.07 | 65.21 | 1.00 | 1 |

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