We present statistical results based on the data set obtained by Cluster when these spacecraft were in the dayside cusp and magnetopause. Forty clearest stagnant exterior cusp (SEC) events have been selected from ~150 cusp crossings from 1 January to 30 April 2001 and from 1 March to 30 April 2002. The identification of the SECs was made on the basis of the following criteria: high-density plasma (comparable to the sheath level) and small or stagnant plasma flow (Vx < 60 km s-1). We found that energetic ions are observed in the high-latitude magnetospheric region for 32 SEC crossings (80%) and energetic electrons are observed on 9 of 40 events (22.5%). The SEC is found to lie predominantly within 1000--1300 magnetic local time (MLT); however, there are some cases where this region extends to both earlier and later MLTs. Twenty-nine SEC events (72.5%) have been found in association with depressed magnetic field. The angular difference between the interplanetary magnetic field (IMF) and local clock angles is a good criterion for 29 SEC events (72.5%). The particle spectra are characterized by a power law, and the power law index is found to be closely related to solar wind velocity. The spectra seem to be harder for higher solar wind velocity. We also found that the higher the solar wind velocity, the higher the ion flux in the SEC region. The magnetic shear angle is the difference between local B vector and IMF clock angle projected on the plane perpendicular to the shock normal. The larger the magnetic shear angle, the more turbulent the magnetic field in the SEC. The turbulence in the SEC region does not affect the power law index, but it is one of the factors controlling of the SEC region. Further, there is no clear relationship found between the power law index and IMF Bz, Dst, or the magnetic shear angle.